A Fourier summation formula for the symmetric space $\mathrm{GL}\left(n\right)/\mathrm{GL}(n-1)$

Flicker, Yuval Z.

Compositio Mathematica, Tome 88 (1993) no. 1, pp. 39-117.

[A] J. Arthur, A trace formula for reductive groups. [A1] I. Terms associated to classes in G(Q), Duke Math. J. 45 (1978), 911-952; [A2] II. Applications of a truncation operator, Compos. Math. 40 (1980), 87-121. | Numdam | MR | Zbl

[B] J. Bernstein, An operator Paley-Wiener theorem, in preparation.

[BD] J. Bernstein, P. Deligne, Le centre de Bernstein, dans Représentation des groupes réductifs sur un corps local, Hermann, Paris (1984). | MR | Zbl

[BZ] J. Bernstein, A. Zelevinskii, [BZ1] Representations of the group GL(n, F) where F is a nonarchimedean local field, Uspekhi Mat. Nauk 31 (1976), 5-70; [BZ2] Induced representations of reductive p-adic groups. I, Ann. Sci. ENS 10 (1977), 441-472. | Numdam | MR | Zbl

[Bi] F. Bien, D-modules and spherical representations, Princeton Univ. Press 39 (1990). | MR | Zbl

[DP] G. Van Dijk, M. Poel, The irreducible unitary GL(n - 1, R)-spherical representations of SL(n, R), Compos. Math. 73 (1990), 1-30. | Numdam | Zbl

[FJ] M. Flensted-Jensen, Discrete series for semi-simple symmetric spaces, Annals of Math. 111 (1980), 253-311. | MR | Zbl

[F] Y. Flicker, [F1] Twisted tensors and Euler products, Bull. Soc. Math. France 116 (1988), 295-313; [F2] On distinguished representations, J. reine angew. Math. 418 (1991), 139-172; [F3] Distinguished representations and a Fourier summation formula, Bull. Soc. Math. France (1992); [F4] Cyclic automorphic forms on a unitary group, preprint. | MR | Zbl

[FK] Y. Flicker, D. Kazhdan, A simple trace formula, J. Analyse Math. 50 (1988), 189-200. | MR | Zbl

[FKS] Y. Flicker, D. Kazhdan, G. Savin, Explicit realization of a metaplectic representation, J. Analyse Math. 55 (1991), 17-39. | MR | Zbl

[GK] I. Gelfand, D. Kazhdan, Representations of GL(n, K) where K is a local field, in Lie groups and their representations, John Wiley and Sons (1975), 95-118. | Zbl

[G] P. Garrett, Decomposition of Eisenstein series. Rankin triple products, Ann. of Math. 125 (1987), 209-235. | MR | Zbl

[GP] B. Gross, D. Prasad, On the decomposition of a representation of SO(n) when restricted to SO(n - 1), preprint. | Zbl

[HK] M. Harris, S. Kudla, The central critical value of a triple product L-function, Ann. of Math. 133 (1991), 605-672. | MR | Zbl

[J] H. Jacquet, [J1] Sur un résultat de Waldspurger, Ann. Sci. ENS. 19 (1986), 185-229; [J2] On the nonvanishing of some L-functions, Proc. Indian Acad. Sci. 97 (1987), 117-155. | MR | Zbl

[JPS] H. Jacquet, I. Piatetski-Shapiro, J. Shalika, Rankin-Selberg convolutions, Amer. J. Math. 105 (1983), 367-464. | MR | Zbl

[JS] H. Jacquet, J. Shalika, [JS1] On Euler products and the classification of automorphic representations, Amer. J. Math. 103 (1981), I: 499-558, II: 777-815; [JS2] Rankin-Selberg convolutions: Archimedean theory; in Festschrift in Honor of I. I. Piatetski-Shapiro, IMCP 2 (1990), 125-207. | Zbl

[L] R. Langlands, On the functional equations satisfied by Eisenstein series, SLN 544 (1976). | MR | Zbl

[M] I. Macdonald, Symmetric functions and Hall polynomials, Oxford, Clarendon Press (1979). | MR | Zbl

[MW] C. Moeglin, J.-L. Waldspurger, [MW1] Le spectre résiduel de GL(n), Ann. Sci. ENS 22 (1989), 605-674; [MW2] Décomposition spectrale et series d'Eisenstein. | Numdam | MR | Zbl

[Mo] L. Morris, Eisenstein series for reductive groups over global function fields, Canad. J. Math. 34 (1982), I: 91-168, II: 1112-1182. | Zbl

[OM] T. Oshima, T. Matsuki, A description of discrete series for semisimple symmetric spaces, Advanced Studies in Pure Math. 4 (1984), 331-390. | MR | Zbl

[PR] I. Piatetski -Shapiro, S. Rallis, Rankin triple L-functions, Compos. Math. 64 (1987), 31-115. | Numdam | MR | Zbl

[P] D. Prasad, [P1] Trilinear forms for representations of GL(2) and local ε-factors, Compos. Math. 75 (1990), 1-46; [P2] Invariant forms for representations of GL2 over a local field, Amer. J. Math. (1993); [P3] On the decomposition of a representation of GL(3) restricted to GL(2) over a p-adic field, Duke Math. J. (1993).

[Sh] F. Shahidi, [Sh1] On certain L-functions, Amer. J. Math. 103 (1981), 297-355; [Sh2] Local coefficients and normalization of intertwining operators for GL(n), Compos. Math. 48 (1983), 271-295. | Numdam | MR | Zbl

[Sh] T. Shintani, On an explicit formula for class 1 "Whittaker functions" on GLn over p-adic fields, Proc. Japan Acad., 52 (1976), 180-182. | MR | Zbl

[T] M. Tadic, Classification of unitary representations in irreducible representations of general linear group, Ann. Sci. ENS 19 (1986), 335-382. | Numdam | MR | Zbl

[Th] E. Thoma, Die Einschränkung der Charaktere von GL(n, q) auf GL(n - 1, q), Math. Z. 119(1971), 321-338. | MR | Zbl

[W] J.-L. Waldspurger, [W1] Correspondence de Shimura, J. Math. Pure Appl. 59 (1980), 1-113; [W2] Sur les coefficients de Fourier des formes modulaires de poids demi-entier, J. Math. Pure Appl. 60 (1981), 375-484; [W3] Sur les valeurs de certaines fonctions L automorphes en leur centre de symetrie, Compos. Math. 54 (1985), 173-242. | Numdam | MR | Zbl

[Z] A. Zelevinsky, Induced representations of reductive p-adic groups II. On irreducible representations of GL(n), Ann. Sci. ENS 13 (1980), 165-210; [Z2] Representations of finite classical groups, SLN 869 (1981). | Numdam | MR | Zbl

[Zh] D.P. Zhelobenko, Compact Lie groups and their representations, American Mathematical Society, Providence, 1973. | MR | Zbl