Representation theory and sheaves on the Bruhat-Tits building

Peter Schneider; Ulrich Stuhler

Publications Mathématiques de l'IHÉS (1997)

  • Volume: 85, page 97-191
  • ISSN: 0073-8301

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Schneider, Peter, and Stuhler, Ulrich. "Representation theory and sheaves on the Bruhat-Tits building." Publications Mathématiques de l'IHÉS 85 (1997): 97-191. <http://eudml.org/doc/104122>.

@article{Schneider1997,
author = {Schneider, Peter, Stuhler, Ulrich},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {representations; -adic groups; Bruhat-Tits buildings; sheaves; Zelevinsky involution; reductive algebraic group},
language = {eng},
pages = {97-191},
publisher = {Institut des Hautes Études Scientifiques},
title = {Representation theory and sheaves on the Bruhat-Tits building},
url = {http://eudml.org/doc/104122},
volume = {85},
year = {1997},
}

TY - JOUR
AU - Schneider, Peter
AU - Stuhler, Ulrich
TI - Representation theory and sheaves on the Bruhat-Tits building
JO - Publications Mathématiques de l'IHÉS
PY - 1997
PB - Institut des Hautes Études Scientifiques
VL - 85
SP - 97
EP - 191
LA - eng
KW - representations; -adic groups; Bruhat-Tits buildings; sheaves; Zelevinsky involution; reductive algebraic group
UR - http://eudml.org/doc/104122
ER -

References

top
  1. [Au1] A.-M. AUBERT, Théorie de Mackey généralisée : Un théorème de décomposition, Preprint, 1992. 
  2. [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). Zbl0827.22005
  3. [Ber] J. BERNSTEIN, Le " centre " de Bernstein, in Bernstein, Deligne, Kazhdan, Vigneras, Représentations des groupes réductifs sur un corps local, Paris, Hermann, 1984. Zbl0599.22016MR86e:22028
  4. [Be2] J. BERNSTEIN, On the support of Plancherel measure, J. Geom. Physics 5 (1988), 663-710. Zbl0725.43010MR91k:22027
  5. [BDK] J. BERNSTEIN, P. DELIGNE, D. KAZHDAN, Trace Paley-Wiener theorem for reductive p-adic groups, J. d'analyse math. 47 (1986), 180-192. Zbl0634.22011MR88g:22016
  6. [BZ] J. BERNSTEIN, A. ZELEVINSKY, Induced representations of reductive p-adic groups I, Ann. sci. ENS 10 (1977), 441-472. Zbl0412.22015MR58 #28310
  7. [Bla] P. BLANC, Projectifs dans la catégorie des G-modules topologiques, C. R. Acad. Sci. Paris 289 (1979), 161-163. Zbl0442.18007MR81m:22007
  8. [Bor] A. BOREL, Linear Algebraic Groups, 2nd Enlarged Edition, Berlin-Heidelberg-New York, Springer 1991. Zbl0726.20030MR92d:20001
  9. [BH] A. BOREL, G. HARDER, Existence of discrete cocompact subgroups of reductive groups over local fields, J. reine angew. Math. 298 (1978), 53-64. Zbl0385.14014MR80b:22022
  10. [BS] A. BOREL, J.-P. SERRE, Cohomologie d'immeubles et de groupes S-arithmétiques, Topology 15 (1976), 211-232. Zbl0338.20055MR56 #5786
  11. [BoT] A. BOREL, J. TITS, Groupes réductifs, Publ. Math. IHES 27 (1965), 55-152. Zbl0145.17402MR34 #7527
  12. [BW] A. BOREL, N. WALLACH, Continuous cohomology, discrete subgroups, and representations of reductive groups, in Ann. Math. Studies 94, Princeton Univ. Press, 1980. Zbl0443.22010MR83c:22018
  13. [Bou] N. BOURBAKI, Groupes et algèbres de Lie, Chap. 4-6, Paris, Masson, 1981. Zbl0483.22001
  14. [Bo2] N. BOURBAKI, Topologie générale, Chap. 5-10, Paris, Hermann, 1974. Zbl0337.54001
  15. [Bro] K. S. BROWN, Buildings, Berlin-Heidelberg-New York, Springer, 1989. Zbl0715.20017MR90e:20001
  16. [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. Zbl0254.14017MR48 #6265
  17. [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. Zbl0421.22010MR81e:22029
  18. [Cas] W. CASSELMAN, Introduction to the theory of admissible representations of p-adic reductive groups, Preprint. 
  19. [Ca2] W. CASSELMAN, A new non-unitary argument for p-adic representations, J. Fac. Sci. Univ. Tokyo 28 (1981), 907-928. Zbl0519.22011MR84e:22018
  20. [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. Zbl0760.22023MR93h:22020
  21. [CLT] C. W. CURTIS, G. I. LEHRER, J. TITS, Spherical Buildings and the Character of the Steinberg Representation, Invent. Math. 58 (1980), 201-210. Zbl0435.20024MR81f:20060
  22. [CR] C. CURTIS, I. REINER, Representation Theory of Finite Groups and Associative Algebras, New York-London, J. Wiley, 1962. Zbl0131.25601MR26 #2519
  23. [DL] P. DELIGNE, G. LUSZTIG, Duality for Representations of a Reductive Group over a Finite Field I, J. Algebra 74 (1982), 284-291. Zbl0482.20027MR83e:20041
  24. [Dix] J. DIXMIER, C*-Algebras, Amsterdam, North-Holland, 1982. 
  25. [Dol] A. DOLD, Lectures on Algebraic Topology, Berlin-Heidelberg-New York, Springer, 1980. Zbl0434.55001MR82c:55001
  26. [GZ] P. GABRIEL, M. ZISMAN, Calculus of Fractions and Homotopy Theory, Berlin-Heidelberg-New York, Springer, 1967. Zbl0186.56802MR35 #1019
  27. [God] R. GODEMENT, Topologie algébrique et théorie des faisceaux, Paris, Hermann, 1964. 
  28. [HCD] HARISH-CHANDRA, G. VAN DIJK, Harmonic Analysis on Reductive p-adic Groups, Lect. Notes Math., vol. 162, Berlin-Heidelberg-New York, Springer, 1970. Zbl0202.41101MR54 #2889
  29. [Har] R. HARTSHORNE, Residues and duality, Lect. Notes Math., vol. 20, Berlin-Heidelberg-New York, Springer, 1966. Zbl0212.26101MR36 #5145
  30. [Hat] A. HATTORI, Rank element of a projective module, Nagoya J. Math. 25 (1965), 113-120. Zbl0142.28001MR31 #226
  31. [KS] M. KASHIWARA, P. SCHAPIRA, Sheaves on Manifolds, Berlin-Heidelberg-New York, Springer, 1990. Zbl0709.18001MR92a:58132
  32. [Kat] S. KATO, Duality for representations of a Hecke algebra, Proc. AMS 119 (1993), 941-946. Zbl0836.22024MR94g:20060
  33. [Ka1] D. KAZHDAN, Cuspidal geometry of p-adic groups, J. d'analyse math. 47 (1986), 1-36. Zbl0634.22009MR88g:22017
  34. [Ka2] D. KAZHDAN, Representations of groups over close local fields, J. d'analyse math. 47 (1986), 175-179. Zbl0634.22010MR88g:22018
  35. [Kot] R. KOTTWITZ, Tamagawa numbers, Ann. Math. 127 (1988), 629-646. Zbl0678.22012MR90e:11075
  36. [MP] A. MOY, G. PRASAD, Unrefined minimal K-types for p-adic groups, Invent. math. 116 (1994), 393-408. Zbl0804.22008MR95f:22023
  37. [PR] G. PRASAD, M. S. RAGHUNATAN, Topological central extensions of semi-simple groups over local fields, Ann. Math. 119 (1984), 143-201. Zbl0552.20025
  38. [Pro] K. PROCTER, The Zelevinsky Duality Conjecture for GLN, Thesis, King's College, London, 1994. 
  39. [Rog] J. ROGAWSKI, An application of the building to orbital integrals, Compositio Math. 42 (1981), 417-423. Zbl0471.22020MR83g:22011
  40. [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. Zbl0780.20026MR94a:22039
  41. [Ser] J.-P. SERRE, Cohomologie des groupes discrets, in Prospects in Mathematics, Ann. Math. Studies 70, 77-169, Princeton Univ. Press, 1971. Zbl0235.22020MR52 #5876
  42. [Sil] A. SILBERGER, Introduction to harmonic analysis on reductive p-adic groups, Princeton Univ. Press, 1979. Zbl0458.22006MR81m:22025
  43. [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. Zbl0415.20035MR80h:20064
  44. [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. Zbl0732.22007MR93c:22034
  45. [Zel] A. ZELEVINSKY, Induced representations of reductive p-adic groups II, Ann. Sci. ENS 13 (1980), 165-210. Zbl0441.22014MR83g:22012

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