Parametrizing nilpotent orbits via Bruhat-Tits theory

Annals of Mathematics

Volumn 156, Issue 1, 2002, Pages 295-332

  DeBacker, Stephen ^a,b  

^a UNIVERSITY OF CHICAGO   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Bruhat Tits building; Nilpotent orbit; Reductive group

Indexed keywords

EID: 0036662706     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.2307/3597191     Document Type: Article

References (28)

1. J.D. Adler, Refined anisotropic K-types and supercuspidal representations, Pacific J. Math. 185 (1998), 1-32.
2. J. Adler and S. Debacker, Some applications of Bruhat-Tits theory to harmonic analysis on the Lie algebra of a reductive p-adic group, Michigan Math. J., to appear.
3. J. Adler and A. Roche, An intertwining result for p-adic groups, Canadian J. Math. 52 (2000), 449-467.
4. P. Bala and R.W. Carter, Classes of unipotent elements in simple algebraic groups. I, Math. Proc. Cambridge Philos. Soc. 79 (1976), 401-425.
5. _, Classes of unipotent elements in simple algebraic groups. II, Math. Proc. Cambridge Philos. Soc. 80 (1976), 1-17.
6. D. Barbasch and A. Moy, Local character expansions, Ann. Sci. École Norm. Sup. 30 (1997), 553-567.
7. A. Borel, Linear Algebraic Groups, second enlarged edition, Grad. Texts in Math. 126, Springer-Verlag, New York, 1991.
8. F. Bruhat and J. TITS, Groupes réductifs sur un corps local, Inst. Hautes Études Sci. Publ. Math. 41 (1972), 5-251.
9. _, 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.
10. R. Carter, Finite Groups of Lie Type. Conjugacy Classes and Complex Characters, Reprint of the 1985 original, Wiley Classics Library, John Wiley & Sons, Ltd., Chichester, 1993.
11. S. Debacker, Homogeneity results for invariant distributions of a reductive p-adic group, Ann. Sci. École Norm. Sup., to appear.
12. Some applications of Bruhat-Tits theory to harmonic analysis on a reductive p-adic group, Michigan Math. J., to appear.
13. Harish-Chandra, Admissible invariant distributions on reductive p-adic groups (Preface and notes by Stephen DeBacker and Paul J. Sally, Jr.), University Lecture Series 16, A.M.S., Providence, RI, 1999.
14. n over a p-adic field), Math. Ann. 208 (1974), 305-322.
15. _, Two conjectures about reductive p-adic groups, in Harmonic Analysis on Homogeneous Spaces, Proc. Sympos. Pure Math. 26 (1973), 377-380.
16. n over a p-adic field, in Orbites Unipotentes et Representations, II, Astérisque 171-172 (1989), 257-273.
17. N. Jacobson, Lie Algebras, republication of the 1962 original, Dover Publ., Inc., New York, 1979.
18. G. Kempf, Instability in invariant theory, Ann. of Math. 108 (1978), 299-316.
19. L. Morris, Fundamental G-strata for classical groups, Duke Math. J. 64 (1991), 501-553.
20. A. Moy and G. Prasad, Jacquet functors and unrefined minimal K-types, Comment. Math. Helv. 71 (1996), 98-121.
21. _, Refined cosets in the Lie algebra of a reductive p-adic group, preprint, 1999.
22. _, Unrefined minimal K-types for p-adic groups, Invent. Math. 116 (1994), 393-408.
23. E. Sommers, A generalization of the Bala-Carter theorem for nilpotent orbits, Internat. Math. Res. Notices 1998, no. 11, 539-562.
24. J. Tits, Reductive groups over p-adic fields, Automorphic Forms, Representations, and L-Functions (A. Borel and W. Casselman, eds.), Proc. Sympos. Pure Math. 33 (1979), 29-69.
25. J.-L. Waldspurger, Homogénéité de certaines distributions sur les groupes p-adiques, Inst. Hautes Études Sci. Publ. Math. 81 (1995), 25-72.
26. _, Intégrales Orbitales Nilpotentes et Endoscopie pour les Groupes Classiques Non Ramifiés, Astérisque 269, 2001.
27. Quelques questions sur les intégrales orbitales unipotentes et les algèbres de Hecke, Bull. Soc. Math. France 124 (1996), 1-34.
28. _, Quelques resultats de finitude concernant les distributions invariantes sur les algèbres de Lie p-adiques, preprint, 1993.