Types and Hecke algebras for principal series representations of split reductive p-adic groups

Annales Scientifiques de l'Ecole Normale Superieure

Volumn 31, Issue 3, 1998, Pages 361-413

  Roche, Alan ^a  

^a PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0032061987     PISSN: 00129593     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0012-9593(98)80139-0     Document Type: Review

References (36)

1. [1] J. D. ADLER, Refined anisotmpic K-types and supercuspidal representations. Pacific Journal of Mathematics, to appear.
2. [2] J. D. ADLER and A. ROCHE, An intertwining result for p-adic groups. Preprint.
3. [3] H. BASS, Algebraic K-Theory. New York, 1968.
4. [4] J. N. BERNSTEIN, Le centre de Bernstein (rédigé par P. Deligne). (Représentations des groupes réductifs sur un corps local, Paris, 1984, pp. 1-32).
5. [5] J. N. BERNSTEIN and A. V. ZELEVINSKY, Induced representations of reductive p-adic groups 1 (Ann. Scient. Éc. Norm. Sup., (4). Vol. 10. 1977, pp. 441-472).
6. [6] A. BOREL, Admissible representations of a semisimple group with vectors fixed under an Iwahori subgroup (Invent. Math., Vol. 35, 1976, pp. 233-259).
7. [7] N. BOURBAKI, Groupes et Algèbres de Lie. Chap. IV, V, VI. Hermann, 1968.
8. [8] F. BRUHAT and J. TITS, Groupes réductifs sur un corps local I. Données radicieltes valuées (Publ. Math. I.H.E.S., Vol. 42, 1972, pp. 1-251).
9. [9] F. BRUHAT and J. TITS, Groupes réductifs sur un corps local II. Schémas en groupes (Publ. Math. I.H.E.S., Vol. 60, 1984, pp. 1-184).
10. [10] C. J. BUSHNELL and P. C. KUTZKO, The admissible dual of GL(N) via compact open subgroups. Annals of Math. Studies 129, Princeton University Press, 1993.
11. [11] C. J. BUSHNELL and P. C. KUTZKO, Semisimple types for GL(N). Preprint.
12. [12] C. J. BUSHNELL and P. C. KUTZKO, The admissible dual of SL(N) I (Ann. Scient. Éc. Norm. Sup., (4), Vol. 26, 1993, pp. 261-279).
13. [13] C. J. BUSHNELL and P. C. KUTZKO, Smooth representations of reductive p-adic groups: structure theory via types. Preprint, February 1996.
14. [14] P. CARTIER, Representations of p-adic groups: A survey. Automorphic forms, representations and L-functions (A. Borel and W. Casselman, ed.). Proc Symposia Pure Math. XXXIII, (Providence, 1979), pp. 111-156.
15. [15] W. CASSELMAN, The unramified principal series of p-adic groups I (Comp. Math., Vol. 40, 1980, pp. 387-406).
16. [16] F. DIGNE and J. MICHEL, Representations of finite groups of Lie type. Cambridge University Press, 1991.
17. [17] D. GOLDSTEIN, Hecke algebra isomorphisms for tamely ramified characters. Ph.D. thesis, University of Chicago, 1990.
18. [18] R. B. HOWLETT and G. I. LEHRER, Induced cuspidal representations and generalised Hecke rings (Inv. Math., Vol. 58, 1980, pp. 37-64).
19. [19] R. HOWE with the collaboration of A. MOY, Harish-Chandra homomorphisms for p-adic groups. Regional Conference Series in Mathematics, no. 59. Providence, 1985.
20. n over p-adic fields (Trans. Am. Math. Soc., Vol. 177, 1973, pp. 275-286).
21. [21] J. E. HUMPHREYS, Linear Algebraic Groups. Springer-Verlag, New York, 1975.
22. [22] J. E. HUMPHREYS, Reflection groups and Coxeter groups. Cambridge University Press, 1990.
23. [23] N. IWAHORI and H. MATSUMOTO, On Some Bruhat decomposition and the structure of the Hecke rings of p-adic Chevalley groups (Publ. Math. I.H.E.S., Vol. 25, 1965, pp. 5-48).
24. [24] D. KAZHDAN and G. LUSZTIG, Proof of the Deligne-Langlands conjecture for Hecke algebras (Invent. Math., Vol. 87, 1987, pp. 153-215).
25. [25] R. P. LANGLANDS, On the classification of representations of real algebraic groups. Representation Theory and Harmonic Analysis on Semisimple Lie Groups (P. J. Sally Jr. and D. Vogan, eds.) Mathematical Surveys and Monographs 31, 101-170. Amer. Math. Soc., Providence, Rhode Island, 1989.
26. [26] G. LUSZTIG, Classification of unipotent representations of simple p-adic groups (Internat. Math. Res. Notices No. 11, 1995, pp. 517-589).
27. [27] L. E. MORRIS, Tamely ramified intertwining algebras (Invent. Math., Vol. 114, 1993, pp. 1-54).
28. [28] L. E. MORRIS, Level zero G-types. Preprint, 1994.
29. [29] A. MOY and G. PRASAD, Jacquet functors and unrefined minimal K-types (Comm. Math. Helv., Vol. 71, 1996, pp. 98-121).
30. [30] M. REEDER, Nonstandard intertwining operators and the structure of un ramified principal series representations (Forum. Math., Vol. 9, no. 4, 1997, pp. 457-516).
31. [31] G. SANJE-MPACKO, Ph.D. thesis, Rutgers University, 1994.
32. [32] T. A. SPRINGER, Reductive Groups. Automorphic forms, representations and L-functions (A. Borel and W. Casselman, ed.). Proc. Symposia in Pure Math. XXXIII, (Providence, 1979), pp. 3-27.
33. [33] T. A. SPRINGER and R. STEINBERG, Conjugacy Classes (Lecture Notes in Math., Vol. 131, Springer-Verlag, Berlin, 1970, pp. 167-266).
34. [34] R. STEINBERG, Endomorphisms of linear algebraic groups (Mem. Amer. Math. Soc., No. 80, 1968).
35. [35] R. STEINBERG, Torsion in reductive groups (Adv. Math., Vol. 15, 1975, pp. 63-92).
36. [36] M. TADIC, Representations of p-adic symplectic groups (Comp. Math., Vol. 90, 1994, pp. 123-181).