Some applications of Bruhat-Tits theory to harmonic analysis on the lie algebra of a reductive p-adic group

Michigan Mathematical Journal

Volumn 50, Issue 2, 2002, Pages 263-286

  Adler, Jeffrey D ^a   DeBacker, Stephen ^a  

^a University of Akron   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036383250     PISSN: 00262285     EISSN: None     Source Type: Journal    
DOI: 10.1307/mmj/1028575734     Document Type: Article

References (27)

1. J. D. Adler, Refined anisotropic K-types and supercuspidal representations, Pacific J. Math. 185 (1998), 1-32.
2. A. Borel, Linear algebraic groups, 2nd ed., Grad. Texts in Math., 126, Springer, New York, 1991.
3. F. Bruhat and J. Tits, Groupes réductifs sur un corps local I: Données radicielles valuées, Inst. Hautes Études Sci. Publ. Math. 41 (1972), 5-251.
4. _, Groupes réductifs sur un corps local II: Schémas en groupes. Existence d'une donnée radicielle valuée, Inst. Hautes Études Sci. Publ. Math. 60 (1984), 197-376.
5. ℓ, ℓ a prime, Ph.D. thesis, Univ. of Chicago, 1997.
6. _, Some applications of Bruhat-Tits theory to harmonic analysis on a reductive p-adic group, Michigan Math. J. 50 (2002), 241-261.
7. Harish-Chandra, Harmonic analysis on reductive p-adic groups (notes by G. Van Dijk), Lecture Notes in Math., 162, Springer, New York, 1970.
8. _, Admissible invariant distributions on reductive p-adic groups (preface and notes by Stephen DeBacker and Paul J. Sally, Jr.), Univ. Lecture Ser., 16, Amer. Math. Soc., Providence, RI, 1999.
9. n over a p-adic field, Pacific J. Math 73 (1977), 479-538.
10. D. Kazhdan, Cuspidal geometry of p-adic groups, J. Anal. Math. 47 (1986), 1-36.
11. G. Kempf, Instability in invariant theory, Ann. of Math. (2) 108 (1978), 299-316.
12. A. Moy and F. Murnaghan, A cuspidality criterion (in preparation).
13. A. Moy and G. Prasad, Unrefined minimal K-types for p-adic groups, Invent. Math. 116 (1994), 393-408.
14. _, Jacquet functors and unrefined minimal K-types, Comment. Math. Helv. 71 (1996), 98-121.
15. F. Murnaghan, Characters of supercuspidal representations of SL(n), Pacific J. Math. 170 (1995), 217-235.
16. _, Local character expansions for supercuspidal representations of U(3), Canad. J. Math. 47 (1995), 606-640.
17. _, Characters of supercuspidal representations of classical groups, Ann. Sci. École Norm. Sup. (4) 29 (1996), 49-105.
18. _, Local character expansions and Shalika germs for GL(n), Math. Ann. 304 (1996), 423-455.
19. _, Local character expansions of admissible representations of p-adic general linear groups, preprint, 2001.
20. _, Germs of characters of admissible representations of p-adic general linear groups, preprint, 2001.
21. G. Prasad and M. S. Raghunathan, Topological central extensions of semi-simple groups over local fields I, Ann. of Math. (2) 119 (1984), 143-201.
22. P. Schneider and U. Stuhler, Representation theory and sheaves on the Bruhat-Tits building, Inst. Hautes Études Sci. Publ. Math. 85 (1997), 97-191.
23. J. Tits, Reductive groups over p-adic fields, Automorphic forms, representations, and L-functions (Corvallis, OR, 1977), Proc. Sympos. Pure Math., 33, pp. 29-69, Amer. Math. Soc., Providence, RI, 1979.
24. M.-E. Vignéras, Cohomology of sheaves on the building and R-representations, Invent. Math. 127 (1997), 349-373.
25. J.-L. Waldspurger, Quelques resultats de finitude concernant les distributions invariantes sur les algèbres de Lie p-adiques, preprint, 1993.
26. _, Homogénéité de certaines distributions sur les groupes p-adiques, Inst. Hautes Études Sci. Publ. Math. 81 (1995), 25-72.
27. _, Intégrales orbitales nilpotentes et endoscopie pour les groupes classiques non ramifiés, Astérisque 269 (2001).