On representations distinguished by unitary groups

Feigon, Brooke; Lapid, Erez; Offen, Omer

doi:10.1007/s10240-012-0040-z

Feigon, Brooke ¹ ; Lapid, Erez ² ; Offen, Omer ³

¹ Department of Mathematics, The City College of New York New York, NY, 10031 USA
² Institute of Mathematics, The Hebrew University of Jerusalem Jerusalem, 91904 Israel
³ Department of Mathematics, Technion-Israel Institute of Technology Haifa, 32000 Israel

Publications Mathématiques de l'IHÉS, Tome 115 (2012), pp. 185-323.

Résumé

Let $E / F$ be a quadratic extension of number fields. We study periods and regularized periods of cusp forms and Eisenstein series on ${GL}_{n} (𝐀_{E})$ over a unitary group of a Hermitian form with respect to $E / F$ . We provide factorization for these periods into locally defined functionals, express these factors in terms of suitably defined local periods and characterize global distinction. We also study in detail the analogous local question and analyze the space of invariant linear forms under a unitary group. be a quadratic extension of number fields. We study periods and regularized periods of cusp forms and Eisenstein series on over a unitary group of a Hermitian form with respect to

MR Zbl

DOI : 10.1007/s10240-012-0040-z

Affiliations des auteurs :

Feigon, Brooke ¹ ; Lapid, Erez ² ; Offen, Omer ³

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Feigon, Brooke; Lapid, Erez; Offen, Omer. On representations distinguished by unitary groups. Publications Mathématiques de l'IHÉS, Tome 115 (2012), pp. 185-323. doi : 10.1007/s10240-012-0040-z. http://archive.numdam.org/articles/10.1007/s10240-012-0040-z/

Bibliographie
Cité par

[AC89.] Arthur, J.; Clozel, L. Simple Algebras, Base Change, and the Advanced Theory of the Trace Formula, Annals of Mathematics Studies, 120, Princeton University Press, Princeton, 1989 (MR 1007299) | MR | Zbl

[AG.] A. Aizenbud and D. Gourevitch, Smooth transfer of Kloosterman integrals (the Archimedean case), Amer. J. Math., to appear. | MR

[AG08.] Aizenbud, A.; Gourevitch, D. Schwartz functions on Nash manifolds, Int. Math. Res. Not., Volume 5 (2008) 37. MR 2418286 (2010g:46124) | MR | Zbl

[AG09a.] Aizenbud, A.; Gourevitch, D. Generalized Harish-Chandra descent, Gelfand pairs, and an Archimedean analog of Jacquet-Rallis’s theorem, Duke Math. J., Volume 149 (2009), pp. 509-567 with an appendix by the authors and Eitan Sayag. MR 2553879 (2011c:22026). | DOI | MR | Zbl

[AG09b.] Aizenbud, A.; Gourevitch, D. Multiplicity one theorem for $(\mathrm{GL}_{n+1}(\Bbb{R}),\mathrm{GL}_{n}(\Bbb{R}))$ , Sel. Math. New Ser., Volume 15 (2009), pp. 271-294 MR 2529937 (2010i:22012) | DOI | MR | Zbl

[AG10.] Aizenbud, A.; Gourevitch, D. The de-Rham theorem and Shapiro lemma for Schwartz function on Nash manifolds, Isr. J. Math., Volume 177 (2010), pp. 155-188 (MR 2684417) | DOI | MR | Zbl

[AGS08.] Aizenbud, A.; Gourevitch, D.; Sayag, E. (GL_n+1(F),GL_n(F)) is a Gelfand pair for any local field F , Compos. Math., Volume 144 (2008), pp. 1504-1524 MR 2474319 (2009k:22022) | DOI | MR | Zbl

[Art78.] Arthur, J. G. A trace formula for reductive groups. I. Terms associated to classes in G(Q), Duke Math. J., Volume 45 (1978), pp. 911-952 MR 518111 (80d:10043) | DOI | MR | Zbl

[Art85.] Arthur, J. A measure on the unipotent variety, Can. J. Math., Volume 37 (1985), pp. 1237-1274 MR 828844 (87m:22049) | DOI | MR | Zbl

[Art86.] Arthur, J. On a family of distributions obtained from orbits, Can. J. Math., Volume 38 (1986), pp. 179-214 MR 835041 (87k:11058) | DOI | MR | Zbl

[Bar89.] Barbasch, D. The unitary dual for complex classical Lie groups, Invent. Math., Volume 96 (1989), pp. 103-176 MR 981739 (90c:22044) | DOI | MR | Zbl

[Bar03.] Baruch, E. M. A proof of Kirillov’s conjecture, Ann. Math. (2), Volume 158 (2003), pp. 207-252 MR 1999922 (2004f:22012) | DOI | MR | Zbl

[BD92.] Brylinski, J.-L.; Delorme, P. Vecteurs distributions H-invariants pour les séries principales généralisées d’espaces symétriques réductifs et prolongement méromorphe d’intégrales d’Eisenstein, Invent. Math., Volume 109 (1992), pp. 619-664 MR 1176208 (93m:22016) | DOI | MR | Zbl

[BD08.] Blanc, P.; Delorme, P. Vecteurs distributions H-invariants de représentations induites, pour un espace symétrique réductif p-adique G/H , Ann. Inst. Fourier (Grenoble), Volume 58 (2008), pp. 213-261 MR 2401221 (2009e:22015) | DOI | Numdam | MR | Zbl

[Ber84.] Bernstein, J. N. P-invariant distributions on GL(N) and the classification of unitary representations of GL(N) (non-Archimedean case), Lie group representations, II (Lecture Notes in Math., 1041), Springer, Berlin (1984), pp. 50-102 (MR 748505) | DOI | MR | Zbl

[BK.] J. Bernstein and B. Krötz, Smooth Fréchet globalizations of Harish-Chandra modules, Israel J. Math., to appear. | MR | Zbl

[BK93.] Bushnell, C. J.; Kutzko, P. C. The Admissible Dual of GL(N) via Compact Open Subgroups, Annals of Mathematics Studies, 129, Princeton University Press, Princeton, 1993 (MR 1204652) | MR | Zbl

[BZ76.] Bernšteĭn, I. N.; Zelevinskiĭ, A. V. Representations of the group GL(n,F), where F is a local non-Archimedean field, Usp. Mat. Nauk, Volume 31 (1976), pp. 5-70 MR 0425030 (54 #12988) no. 3(189) | MR | Zbl

[BZ77.] Bernstein, I. N.; Zelevinsky, A. V. Induced representations of reductive $\mathfrak{p}$-adic groups. I, Ann. Sci. Éc. Norm. Super. (4), Volume 10 (1977), pp. 441-472 MR 0579172 (58 #28310) | Numdam | MR | Zbl

[CD94.] Carmona, J.; Delorme, P. Base méromorphe de vecteurs distributions H-invariants pour les séries principales généralisées d’espaces symétriques réductifs: equation fonctionnelle, J. Funct. Anal., Volume 122 (1994), pp. 152-221 MR 1274587 (95g:22021) | DOI | MR | Zbl

[Châ99.] Châu, N. B. Le lemme fondamental de Jacquet et Ye en caractéristique positive, Duke Math. J., Volume 96 (1999), pp. 473-520 MR 1671212 (2000f:11059) | DOI | MR | Zbl

[CO07.] Chinta, G.; Offen, O. Unitary periods, Hermitian forms and points on flag varieties, Math. Ann., Volume 339 (2007), pp. 891-913 MR 2341906 (2009e:11070) | DOI | MR | Zbl

[CS80.] Casselman, W.; Shalika, J. The unramified principal series of p-adic groups. II. The Whittaker function, Compos. Math., Volume 41 (1980), pp. 207-231 MR 581582 (83i:22027) | Numdam | MR | Zbl

[CS98.] Casselman, W.; Shahidi, F. On irreducibility of standard modules for generic representations, Ann. Sci. Éc. Norm. Super. (4), Volume 31 (1998), pp. 561-589 MR 1634020 (99f:22028) | Numdam | MR | Zbl

[DKV84.] Deligne, P.; Kazhdan, D.; Vignéras, M.-F. Représentations des algèbres centrales simples p-adiques, Representations of Reductive Groups over a Local Field, Travaux en Cours, Hermann, Paris (1984), pp. 33-117 (MR 771672) | Zbl

[FJŌS88.] Flensted-Jensen, M.; Ōshima, T.; Schlichtkrull, H. Boundedness of certain unitarizable Harish-Chandra modules, Representations of Lie groups, Kyoto, Hiroshima, 1986 (Adv. Stud. Pure Math., 14), Academic Press, Boston (1988), pp. 651-660 (MR 1039855) | Zbl

[GK75.] Gel’fand, I. M.; Kajdan, D. A. Representations of the group GL(n,K) where K is a local field, Lie Groups and Their Representations, Halsted, New York (1975), pp. 95-118 (MR 0404534)

[Gow84.] Gow, R. Two multiplicity-free permutation representations of the general linear group GL(n,q ²), Math. Z., Volume 188 (1984), pp. 45-54 MR 767361 (86a:20008) | DOI | MR | Zbl

[Hen10.] Henniart, G. Induction automorphe pour $\mathrm{GL}(n,\Bbb{C})$ , J. Funct. Anal., Volume 258 (2010), pp. 3082-3096 MR 2595735 (2011e:22028) | DOI | MR | Zbl

[HH95.] Henniart, G.; Herb, R. Automorphic induction for GL(n) (over local non-Archimedean fields), Duke Math. J., Volume 78 (1995), pp. 131-192 MR 1328755 (96i:22038) | DOI | MR | Zbl

[Hir99.] Hironaka, Y. Spherical functions and local densities on Hermitian forms, J. Math. Soc. Jpn., Volume 51 (1999), pp. 553-581 MR 1691493 (2000c:11064) | DOI | MR | Zbl

[HLR86.] Harder, G.; Langlands, R. P.; Rapoport, M. Algebraische Zyklen auf Hilbert-Blumenthal-Flächen, J. Reine Angew. Math., Volume 366 (1986), pp. 53-120 MR 833013 (87k:11066) | MR | Zbl

[HM98.] Hakim, J.; Mao, Z. Supercuspidal representations of GL(n) distinguished by a unitary subgroup, Pac. J. Math., Volume 185 (1998), pp. 149-162 MR 1653208 (99j:22023) | DOI | MR | Zbl

[HM02a.] Hakim, J.; Murnaghan, F. Globalization of distinguished supercuspidal representations of GL(n), Can. Math. Bull., Volume 45 (2002), pp. 220-230 MR 1904086 (2003f:22022) | DOI | MR | Zbl

[HM02b.] Hakim, J.; Murnaghan, F. Tame supercuspidal representations of GL(n) distinguished by a unitary group, Compos. Math., Volume 133 (2002), pp. 199-244 MR 1923582 (2003g:22019) | DOI | MR | Zbl

[HW93.] Helminck, A. G.; Wang, S. P. On rationality properties of involutions of reductive groups, Adv. Math., Volume 99 (1993), pp. 26-96 MR 1215304 (94d:20051) | DOI | MR | Zbl

[Ich08.] Ichino, A. Trilinear forms and the central values of triple product L-functions, Duke Math. J., Volume 145 (2008), pp. 281-307 MR 2449948 (2009i:11066) | DOI | MR | Zbl

[II10.] Ichino, A.; Ikeda, T. On the periods of automorphic forms on special orthogonal groups and the Gross-Prasad conjecture, Geom. Funct. Anal., Volume 19 (2010), pp. 1378-1425 (MR 2585578) | DOI | MR | Zbl

[Jac67.] Jacquet, H. Fonctions de Whittaker associées aux groupes de Chevalley, Bull. Soc. Math. Fr., Volume 95 (1967), pp. 243-309 MR 0271275 (42 #6158) | Numdam | MR | Zbl

[Jac92.] Jacquet, H. Relative Kloosterman integrals for GL(3). II, Can. J. Math., Volume 44 (1992), pp. 1220-1240 MR 1192415 (94c:11048) | DOI | MR | Zbl

[Jac95.] Jacquet, H. The continuous spectrum of the relative trace formula for GL(3) over a quadratic extension, Isr. J. Math., Volume 89 (1995), pp. 1-59 MR 1324453 (96a:22029) | DOI | MR | Zbl

[Jac98.] Jacquet, H. A theorem of density for Kloosterman integrals, Asian J. Math., Volume 2 (1998), pp. 759-778 Mikio Sato: a great Japanese mathematician of the twentieth century. MR 1734128 (2001e:11054) | MR | Zbl

[Jac01.] Jacquet, H. Factorization of period integrals, J. Number Theory, Volume 87 (2001), pp. 109-143 MR 1816039 (2002a:11050) | DOI | MR | Zbl

[Jac02.] Jacquet, H. Transfert lisse d’intégrales de Kloosterman, C. R. Math. Acad. Sci. Paris, Volume 335 (2002), pp. 229-232 MR 1933663 (2003k:11082) | DOI | MR | Zbl

[Jac03a.] Jacquet, H. Facteurs de transfert pour les intégrales de Kloosterman, C. R. Math. Acad. Sci. Paris, Volume 336 (2003), pp. 121-124 MR 1969564 (2004e:11052) | DOI | MR | Zbl

[Jac03b.] Jacquet, H. Smooth transfer of Kloosterman integrals, Duke Math. J., Volume 120 (2003), pp. 121-152 MR 2010736 (2005a:11066) | DOI | MR | Zbl

[Jac04a.] Jacquet, H. Integral representation of Whittaker functions, Contributions to Automorphic Forms, Geometry, and Number Theory, Johns Hopkins Univ. Press, Baltimore (2004), pp. 373-419 (MR 2058615) | Zbl

[Jac04b.] Jacquet, H. Kloosterman identities over a quadratic extension, Ann. Math. (2), Volume 160 (2004), pp. 755-779 MR 2123938 (2006d:11051) | DOI | MR | Zbl

[Jac05a.] Jacquet, H. Kloosterman identities over a quadratic extension. II, Ann. Sci. Éc. Norm. Super. (4), Volume 38 (2005), pp. 609-669 MR 2172953 (2006j:11070) | Numdam | MR | Zbl

[Jac05b.] Jacquet, H. Kloosterman integrals for $\mathrm{GL}(2,\Bbb{R})$ , Pure Appl. Math. Q., Volume 1 (2005), pp. 257-289 MR 2194725 (2007j:22019) no. 2, part 1 | MR | Zbl

[Jac09.] Jacquet, H. Archimedean Rankin-Selberg integrals, Automorphic Forms and L-functions II (Local Aspects, Contemp. Math., 489), Amer. Math. Soc., Providence (2009), pp. 57-172 (MR 2533003) | DOI | Zbl

[Jac10.] Jacquet, H. Distinction by the quasi-split unitary group, Isr. J. Math., Volume 178 (2010), pp. 269-324 MR 2733072 (2011k:11073) | DOI | MR | Zbl

[JLR99.] Jacquet, H.; Lapid, E.; Rogawski, J. Periods of automorphic forms, J. Am. Math. Soc., Volume 12 (1999), pp. 173-240 MR 1625060 (99c:11056) | DOI | MR | Zbl

[JLR04.] Jacquet, H.; Lapid, E.; Rallis, S. A spectral identity for skew symmetric matrices, Contributions to Automorphic Forms, Geometry, and Number Theory, Johns Hopkins Univ. Press, Baltimore (2004), pp. 421-455 (MR 2058616) | MR | Zbl

[JPSS83.] Jacquet, H.; Piatetskii-Shapiro, I. I.; Shalika, J. A. Rankin-Selberg convolutions, Am. J. Math., Volume 105 (1983), pp. 367-464 MR 701565 (85g:11044) | DOI | MR | Zbl

[JS81a.] Jacquet, H.; Shalika, J. A. On Euler products and the classification of automorphic forms. II, Am. J. Math., Volume 103 (1981), pp. 777-815 MR 623137 (82m:10050b) | DOI | MR | Zbl

[JS81b.] Jacquet, H.; Shalika, J. A. On Euler products and the classification of automorphic representations. I, Am. J. Math., Volume 103 (1981), pp. 499-558 MR 618323 (82m:10050a) | DOI | MR | Zbl

[JS83.] Jacquet, H.; Shalika, J. The Whittaker models of induced representations, Pac. J. Math., Volume 109 (1983), pp. 107-120 MR 716292 (85h:22023) | MR | Zbl

[JS90.] Jacquet, H.; Shalika, J. Rankin-Selberg convolutions: Archimedean theory, Festschrift in Honor of I. I. Piatetski-Shapiro on the Occasion of His Sixtieth Birthday, Part I (Israel Math. Conf. Proc., 2), Weizmann, Jerusalem (1990), pp. 125-207 MR 1159102 (93d:22022) | Zbl

[JY90.] Jacquet, H.; Ye, Y. Une remarque sur le changement de base quadratique, C. R. Acad. Sci. Paris Sér. I Math., Volume 311 (1990), pp. 671-676 MR 1081622 (92j:11046) | MR | Zbl

[JY92.] Jacquet, H.; Ye, Y. Relative Kloosterman integrals for GL(3), Bull. Soc. Math. Fr., Volume 120 (1992), pp. 263-295 MR 1180831 (94c:11047) | Numdam | MR | Zbl

[JY96.] Jacquet, H.; Ye, Y. Distinguished representations and quadratic base change for GL(3), Trans. Am. Math. Soc., Volume 348 (1996), pp. 913-939 MR 1340178 (96h:11041) | DOI | MR | Zbl

[JY99.] Jacquet, H.; Ye, Y. Germs of Kloosterman integrals for GL(3), Trans. Am. Math. Soc., Volume 351 (1999), pp. 1227-1255 MR 1443878 (99j:11053) | DOI | MR | Zbl

[Lag08.] Lagier, N. Terme constant de fonctions sur un espace symétrique réductif p-adique, J. Funct. Anal., Volume 254 (2008), pp. 1088-1145 MR 2381204 (2009d:22013) | DOI | MR | Zbl

[Lap06.] Lapid, E. M. On the fine spectral expansion of Jacquet’s relative trace formula, J. Inst. Math. Jussieu, Volume 5 (2006), pp. 263-308 MR 2225043 (2007d:11059) | DOI | MR | Zbl

[Lap08.] Lapid, E. M. A remark on Eisenstein series, Eisenstein Series and Applications (Progr. Math., 258), Birkhäuser, Boston (2008), pp. 239-249 (MR 2402686) | DOI | Zbl

[LL79.] Labesse, J.-P.; Langlands, R. P. L-indistinguishability for SL(2), Can. J. Math., Volume 31 (1979), pp. 726-785 MR 540902 (81b:22017) | DOI | MR | Zbl

[LM.] E. Lapid and A. Mínguez, On a determinantal formula of Tadić, Amer. J. Math., to appear. | Zbl

[LM09a.] Lapid, E.; Mao, Z. On the asymptotics of Whittaker functions, Represent. Theory, Volume 13 (2009), pp. 63-81 MR 2495561 (2010b:22024) | DOI | MR | Zbl

[LM09b.] Lapid, E.; Müller, W. Spectral asymptotics for arithmetic quotients of $\mathrm{SL}(n,\Bbb{R})/\mathrm{SO}(n)$ , Duke Math. J., Volume 149 (2009), pp. 117-155 (MR 2541128) | DOI | MR | Zbl

[LO07.] Lapid, E.; Offen, O. Compact unitary periods, Compos. Math., Volume 143 (2007), pp. 323-338 MR 2309989 (2008g:11091) | MR | Zbl

[LR00.] Lapid, E.; Rogawski, J. Stabilization of periods of Eisenstein series and Bessel distributions on GL(3) relative to U(3), Doc. Math., Volume 5 (2000), pp. 317-350 (electronic). MR 1767567 (2002b:11068) | MR | Zbl

[LR01.] Lapid, E.; Rogawski, J. Periods of Eisenstein series, C. R. Acad. Sci. Paris Sér. I Math., Volume 333 (2001), pp. 513-516 MR 1860921 (2002k:11072) | DOI | MR | Zbl

[LR03.] Lapid, E. M.; Rogawski, J. D. Periods of Eisenstein series: the Galois case, Duke Math. J., Volume 120 (2003), pp. 153-226 MR 2010737 (2004m:11077) | DOI | MR | Zbl

[MW86.] Mœglin, C.; Waldspurger, J.-L. Sur l’involution de Zelevinski, J. Reine Angew. Math., Volume 372 (1986), pp. 136-177 MR 863522 (88c:22019) | MR | Zbl

[MW89.] Mœglin, C.; Waldspurger, J.-L. Le spectre résiduel de GL(n), Ann. Sci. Éc. Norm. Super. (4), Volume 22 (1989), pp. 605-674 MR 1026752 (91b:22028) | Numdam | Zbl

[Ngô99.] Ngô, B. C. Faisceaux pervers, homomorphisme de changement de base et lemme fondamental de Jacquet et Ye, Ann. Sci. Éc. Norm. Super. (4), Volume 32 (1999), pp. 619-679 MR 1710755 (2001g:11076) | Numdam | Zbl

[Off07.] Offen, O. Stable relative Bessel distributions on GL(n) over a quadratic extension, Am. J. Math., Volume 129 (2007), pp. 1183-1226 MR 2354318 (2009j:22021) | DOI | MR | Zbl

[Off09.] Offen, O. Unitary periods and Jacquet’s relative trace formula, Automorphic Forms and L-functions I (Global Aspects, Contemp. Math., 488), Amer. Math. Soc., Providence (2009), pp. 183-236 (MR 2522031) | DOI | Zbl

[Pou72.] Skovhus Poulsen, N. On C ^∞-vectors and intertwining bilinear forms for representations of Lie groups, J. Funct. Anal., Volume 9 (1972), pp. 87-120 MR 0310137 (46 #9239) | DOI | Zbl

[Pra01.] Prasad, D. On a conjecture of Jacquet about distinguished representations of GL(n), Duke Math. J., Volume 109 (2001), pp. 67-78 MR 1844204 (2002g:22036) | DOI | MR | Zbl

[Sar04.] P. Sarnak, A letter to Cathleen Morawetz, http://www.math.princeton.edu/sarnak (2004).

[Sha84.] Shahidi, F. Fourier transforms of intertwining operators and Plancherel measures for GL(n), Am. J. Math., Volume 106 (1984), pp. 67-111 MR 729755 (86b:22031) | DOI | MR | Zbl

[Sha85.] Shahidi, F. Local coefficients as Artin factors for real groups, Duke Math. J., Volume 52 (1985), pp. 973-1007 MR 816396 (87m:11049) | DOI | MR | Zbl

[Sha90.] Shahidi, F. A proof of Langlands’ conjecture on Plancherel measures; complementary series for p-adic groups, Ann. Math. (2), Volume 132 (1990), pp. 273-330 MR 1070599 (91m:11095) | DOI | MR | Zbl

[Shi76.] Shintani, T. Two remarks on irreducible characters of finite general linear groups, J. Math. Soc. Jpn., Volume 28 (1976), pp. 396-414 MR 0414730 (54 #2825) | DOI | MR | Zbl

[Spr85.] Springer, T. A. Some results on algebraic groups with involutions, Algebraic Groups and Related Topics (Adv. Stud. Pure Math., 6), North-Holland, Amsterdam (1985), pp. 525-543 (MR 803346) | Zbl

[Tad86.] Tadić, M. Classification of unitary representations in irreducible representations of general linear group (non-Archimedean case), Ann. Sci. Éc. Norm. Super. (4), Volume 19 (1986), pp. 335-382 MR 870688 (88b:22021) | Numdam | Zbl

[vdBD88.] Ban, E.; Delorme, P. Quelques propriétés des représentations sphériques pour les espaces symétriques réductifs, J. Funct. Anal., Volume 80 (1988), pp. 284-307 MR 961900 (89j:22025) | DOI | MR | Zbl

[Wal85.] Waldspurger, J.-L. Sur les valeurs de certaines fonctions L automorphes en leur centre de symétrie, Compos. Math., Volume 54 (1985), pp. 173-242 MR 783511 (87g:11061b) | Numdam | MR | Zbl

[Wal92.] Wallach, N. R. Real Reductive Groups. II, Pure and Applied Mathematics, 132, Academic Press, Boston (1992) (MR 1170566) | Zbl

[Wei82.] Weil, A. Adeles and Algebraic Groups, Progress in Mathematics, 23, Birkhäuser, Boston (1982) (With appendices by M. Demazure and Takashi Ono. MR 670072) | DOI | Zbl

[Ye88.] Ye, Y. Kloosterman integrals and base change, Number Theory and Its Applications in China (Contemp. Math., 77), Amer. Math. Soc., Providence (1988), pp. 163-170 (MR 973234) | DOI | Zbl

[Ye89.] Ye, Y. Kloosterman integrals and base change for GL(2), J. Reine Angew. Math., Volume 400 (1989), pp. 57-121 MR 1013725 (90i:11134) | MR | Zbl

[Ye93.] Ye, Y. The fundamental lemma of a relative trace formula for GL(3), Compos. Math., Volume 89 (1993), pp. 121-162 MR 1255692 (95b:22023) | Numdam | Zbl

[Ye94.] Ye, Y. An integral transform and its applications, Math. Ann., Volume 300 (1994), pp. 405-417 MR 1304430 (95j:11045) | DOI | MR | Zbl

[Ye95.] Ye, Y. The lifting of Kloosterman sums, J. Number Theory, Volume 51 (1995), pp. 275-287 MR 1326749 (97a:11126) | DOI | MR | Zbl

[Ye98.] Ye, Y. A Kloosterman sum in a relative trace formula for GL₄ , Represent. Theory, Volume 2 (1998), pp. 370-392 (electronic). MR 1641835 (99j:11092) | DOI | MR | Zbl

[Zel80.] Zelevinsky, A. V. Induced representations of reductive $𝔭$ -adic groups. II. On irreducible representations of $GL (n)$ , Ann. Sci. Éc. Norm. Super. (4), Volume 13 (1980), pp. 165-210 MR 584084 (83g:22012) | Numdam | MR | Zbl

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