Representation theory and sheaves on the Bruhat-Tits building
Publications Mathématiques de l'IHÉS, Volume 85  (1997), p. 97-191
@article{PMIHES_1997__85__97_0,
     author = {Schneider, Peter and Stuhler, Ulrich},
     title = {Representation theory and sheaves on the Bruhat-Tits building},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {85},
     year = {1997},
     pages = {97-191},
     zbl = {0892.22012},
     mrnumber = {98m:22023},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1997__85__97_0}
}
Schneider, Peter; Stuhler, Ulrich. Representation theory and sheaves on the Bruhat-Tits building. Publications Mathématiques de l'IHÉS, Volume 85 (1997) , pp. 97-191. http://www.numdam.org/item/PMIHES_1997__85__97_0/

[Au1] A.-M. Aubert, Théorie de Mackey généralisée : Un théorème de décomposition, Preprint, 1992.

[Au2] A.-M. Aubert, Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d'un groupe réductif p-adique, Transact. AMS 347 (1995), 2179-2189 ; Erratum, ibid. 348 (1996). | Zbl 0827.22005

[Ber] J. Bernstein, Le " centre " de Bernstein, in Bernstein, Deligne, Kazhdan, Vigneras, Représentations des groupes réductifs sur un corps local, Paris, Hermann, 1984. | MR 86e:22028 | Zbl 0599.22016

[Be2] J. Bernstein, On the support of Plancherel measure, J. Geom. Physics 5 (1988), 663-710. | MR 91k:22027 | Zbl 0725.43010

[BDK] J. Bernstein, P. Deligne, D. Kazhdan, Trace Paley-Wiener theorem for reductive p-adic groups, J. d'analyse math. 47 (1986), 180-192. | MR 88g:22016 | Zbl 0634.22011

[BZ] J. Bernstein, A. Zelevinsky, Induced representations of reductive p-adic groups I, Ann. sci. ENS 10 (1977), 441-472. | Numdam | MR 58 #28310 | Zbl 0412.22015

[Bla] P. Blanc, Projectifs dans la catégorie des G-modules topologiques, C. R. Acad. Sci. Paris 289 (1979), 161-163. | MR 81m:22007 | Zbl 0442.18007

[Bor] A. Borel, Linear Algebraic Groups, 2nd Enlarged Edition, Berlin-Heidelberg-New York, Springer 1991. | MR 92d:20001 | Zbl 0726.20030

[BH] A. Borel, G. Harder, Existence of discrete cocompact subgroups of reductive groups over local fields, J. reine angew. Math. 298 (1978), 53-64. | MR 80b:22022 | Zbl 0385.14014

[BS] A. Borel, J.-P. Serre, Cohomologie d'immeubles et de groupes S-arithmétiques, Topology 15 (1976), 211-232. | MR 56 #5786 | Zbl 0338.20055

[BoT] A. Borel, J. Tits, Groupes réductifs, Publ. Math. IHES 27 (1965), 55-152. | Numdam | MR 34 #7527 | Zbl 0145.17402

[BW] A. Borel, N. Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, in Ann. Math. Studies 94, Princeton Univ. Press, 1980. | MR 83c:22018 | Zbl 0443.22010

[Bou] N. Bourbaki, Groupes et algèbres de Lie, Chap. 4-6, Paris, Masson, 1981. | Zbl 0483.22001

[Bo2] N. Bourbaki, Topologie générale, Chap. 5-10, Paris, Hermann, 1974. | Zbl 0337.54001

[Bro] K. S. Brown, Buildings, Berlin-Heidelberg-New York, Springer, 1989. | MR 90e:20001 | Zbl 0715.20017

[BT] F. Bruhat, J. Tits, Groupes réductifs sur un corps local I. Données radicielles valuées, Publ. Math. IHES 41 (1972), 5-251 ; II. Schémas en groupes. Existence d'une donnée radicielle valuée, Publ. Math. IHES 60 (1984), 5-184. | Numdam | MR 48 #6265 | Zbl 0254.14017

[Car] P. Cartier, Representations of p-adic groups : A survey, in Automorphic Forms, Representations and L-Functions, Proc. Symp. Pure Math. 33 (1), 111-155, American Math. Soc., 1979. | MR 81e:22029 | Zbl 0421.22010

[Cas] W. Casselman, Introduction to the theory of admissible representations of p-adic reductive groups, Preprint.

[Ca2] W. Casselman, A new non-unitary argument for p-adic representations, J. Fac. Sci. Univ. Tokyo 28 (1981), 907-928. | MR 84e:22018 | Zbl 0519.22011

[Clo] L. Clozel, Invariant harmonic analysis on the Schwartz space of a reductive p-adic group, in Harmonic Analysis on Reductive Groups (Eds. Barker, Sally), Progress in Math. 101, 101-121, Boston-Basel-Berlin, Birkhäuser, 1991. | MR 93h:22020 | Zbl 0760.22023

[CLT] C. W. Curtis, G. I. Lehrer, J. Tits, Spherical Buildings and the Character of the Steinberg Representation, Invent. Math. 58 (1980), 201-210. | MR 81f:20060 | Zbl 0435.20024

[CR] C. Curtis, I. Reiner, Representation Theory of Finite Groups and Associative Algebras, New York-London, J. Wiley, 1962. | MR 26 #2519 | Zbl 0131.25601

[DL] P. Deligne, G. Lusztig, Duality for Representations of a Reductive Group over a Finite Field I, J. Algebra 74 (1982), 284-291. | MR 83e:20041 | Zbl 0482.20027

[Dix] J. Dixmier, C*-Algebras, Amsterdam, North-Holland, 1982.

[Dol] A. Dold, Lectures on Algebraic Topology, Berlin-Heidelberg-New York, Springer, 1980. | MR 82c:55001 | Zbl 0434.55001

[GZ] P. Gabriel, M. Zisman, Calculus of Fractions and Homotopy Theory, Berlin-Heidelberg-New York, Springer, 1967. | MR 35 #1019 | Zbl 0186.56802

[God] R. Godement, Topologie algébrique et théorie des faisceaux, Paris, Hermann, 1964.

[HCD] Harish-Chandra, G. Van Dijk, Harmonic Analysis on Reductive p-adic Groups, Lect. Notes Math., vol. 162, Berlin-Heidelberg-New York, Springer, 1970. | MR 54 #2889 | Zbl 0202.41101

[Har] R. Hartshorne, Residues and duality, Lect. Notes Math., vol. 20, Berlin-Heidelberg-New York, Springer, 1966. | MR 36 #5145 | Zbl 0212.26101

[Hat] A. Hattori, Rank element of a projective module, Nagoya J. Math. 25 (1965), 113-120. | MR 31 #226 | Zbl 0142.28001

[KS] M. Kashiwara, P. Schapira, Sheaves on Manifolds, Berlin-Heidelberg-New York, Springer, 1990. | MR 92a:58132 | Zbl 0709.18001

[Kat] S. Kato, Duality for representations of a Hecke algebra, Proc. AMS 119 (1993), 941-946. | MR 94g:20060 | Zbl 0836.22024

[Ka1] D. Kazhdan, Cuspidal geometry of p-adic groups, J. d'analyse math. 47 (1986), 1-36. | MR 88g:22017 | Zbl 0634.22009

[Ka2] D. Kazhdan, Representations of groups over close local fields, J. d'analyse math. 47 (1986), 175-179. | MR 88g:22018 | Zbl 0634.22010

[Kot] R. Kottwitz, Tamagawa numbers, Ann. Math. 127 (1988), 629-646. | MR 90e:11075 | Zbl 0678.22012

[MP] A. Moy, G. Prasad, Unrefined minimal K-types for p-adic groups, Invent. math. 116 (1994), 393-408. | MR 95f:22023 | Zbl 0804.22008

[PR] G. Prasad, M. S. Raghunatan, Topological central extensions of semi-simple groups over local fields, Ann. Math. 119 (1984), 143-201. | Zbl 0552.20025

[Pro] K. Procter, The Zelevinsky Duality Conjecture for GLN, Thesis, King's College, London, 1994.

[Rog] J. Rogawski, An application of the building to orbital integrals, Compositio Math. 42 (1981), 417-423. | Numdam | MR 83g:22011 | Zbl 0471.22020

[SS] P. Schneider, U. Stuhler, Resolutions for smooth representations of the general linear group over a local field, J. reine angew. Math. 436 (1993), 19-32. | MR 94a:22039 | Zbl 0780.20026

[Ser] J.-P. Serre, Cohomologie des groupes discrets, in Prospects in Mathematics, Ann. Math. Studies 70, 77-169, Princeton Univ. Press, 1971. | MR 52 #5876 | Zbl 0235.22020

[Sil] A. Silberger, Introduction to harmonic analysis on reductive p-adic groups, Princeton Univ. Press, 1979. | MR 81m:22025 | Zbl 0458.22006

[Tit] J. Tits, Reductive groups over local fields, in Automorphic Forms, Representations and L-Functions, Proc. Symp. Pure Math. 33 (1), 29-69, American Math. Soc., 1979. | MR 80h:20064 | Zbl 0415.20035

[Vig] M.-F. Vigneras, On formal dimensions for reductive p-adic groups, in Festschrift in honor of I. I. Piatetski-Shapiro (Eds. Gelbart, Howe, Sarnak), Part I, 225-266, Israel Math. Conf. Proc. 2, Jerusalem, Weizmann Science Press, 1990. | MR 93c:22034 | Zbl 0732.22007

[Zel] A. Zelevinsky, Induced representations of reductive p-adic groups II, Ann. Sci. ENS 13 (1980), 165-210. | Numdam | MR 83g:22012 | Zbl 0441.22014