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

 Access to full text

 Full (PDF)

1. [1] J. D. ADLER, Refined anisotropic K-types and supercuspidal representations. Pacific Journal of Mathematics, to appear. Zbl0924.22015
2. [2] J. D. ADLER and A. ROCHE, An intertwining result for p-adic groups. Preprint. Zbl1160.22304
3. [3] H. BASS, Algebraic K-Theory, New York, 1968. Zbl0174.30302MR40 #2736
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). Zbl0599.22016MR86e:22028
5. [5] J. N. BERNSTEIN and A. V. ZELEVINSKY, Induced representations of reductive p-adic groups I (Ann. Scient. Éc. Norm. Sup., (4), Vol. 10, 1977, pp. 441-472). Zbl0412.22015MR58 #28310
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). Zbl0334.22012MR56 #3196
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 radicielles valuées (Publ. Math. I.H.E.S., Vol. 42, 1972, pp. 1-251). Zbl0254.14017MR48 #6265
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). Zbl0597.14041
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. Zbl0787.22016MR94h:22007
11. [11] C. J. BUSHNELL and P. C. KUTZKO, Semisimple types for GL(N). Preprint. Zbl0835.22009
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). Zbl0787.22017MR94a:22033
13. [13] C. J. BUSHNELL and P. C. KUTZKO, Smooth representations of reductive p-adic groups : structure theory via types. Preprint, February 1996. Zbl0911.22014
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. Zbl0421.22010MR81e:22029
15. [15] W. CASSELMAN, The unramified principal series of p-adic groups I (Comp. Math., Vol. 40, 1980, pp. 387-406). Zbl0472.22004MR83a:22018
16. [16] F. DIGNE and J. MICHEL, Representations of finite groups of Lie type. Cambridge University Press, 1991. Zbl0815.20014MR92g:20063
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). Zbl0435.20023MR81j:20017
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. Zbl0593.22014MR87h:22023
20. [20] R. HOWE, Principal series of GLn over p-adic fields (Trans. Am. Math. Soc., Vol. 177, 1973, pp. 275-286). Zbl0257.22018MR48 #6324
21. [21] J. E. HUMPHREYS, Linear Algebraic Groups. Springer-Verlag, New York, 1975. Zbl0325.20039MR53 #633
22. [22] J. E. HUMPHREYS, Reflection groups and Coxeter groups. Cambridge University Press, 1990. Zbl0725.20028MR92h:20002
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). Zbl0228.20015MR32 #2486
24. [24] D. KAZHDAN and G. LUSZTIG, Proof of the Deligne-Langlands conjecture for Hecke algebras (Invent. Math., Vol. 87, 1987, pp. 153-215). Zbl0613.22004MR88d:11121
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. Zbl0741.22009MR91e:22017
26. [26] G. LUSZTIG, Classification of unipotent representations of simple p-adic groups (Internat. Math. Res. Notices No. 11, 1995, pp. 517-589). Zbl0872.20041MR98b:22034
27. [27] L. E. MORRIS, Tamely ramified intertwining algebras (Invent. Math., Vol. 114, 1993, pp. 1-54). Zbl0854.22022MR94g:22035
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). Zbl0860.22006MR97c:22021
30. [30] M. REEDER, Nonstandard intertwining operators and the structure of unramified principal series representations (Forum. Math., Vol. 9, no. 4, 1997, pp. 457-516). Zbl0882.22020MR98j:22028
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. Zbl0416.20034MR80h:20062
33. [33] T. A. SPRINGER and R. STEINBERG, Conjugacy Classes (Lecture Notes in Math., Vol. 131, Springer-Verlag, Berlin, 1970, pp. 167-266). Zbl0249.20024MR42 #3091
34. [34] R. STEINBERG, Endomorphisms of linear algebraic groups (Mem. Amer. Math. Soc., No. 80, 1968). Zbl0164.02902MR37 #6288
35. [35] R. STEINBERG, Torsion in reductive groups (Adv. Math., Vol. 15, 1975, pp. 63-92). Zbl0312.20026MR50 #7369
36. [36] M. TADIC, Representations of p-adic symplectic groups (Comp. Math., Vol. 90, 1994, pp. 123-181). Zbl0797.22008MR95a:22025

1. J.-F. Dat, Types et inductions pour les représentations modulaires des groupes $p$-adiques. With an appendix by Marie-France Vignéras
2. Laure Blasco, Corinne Blondel, Types induits des paraboliques maximaux de $S{p}_4\left(F\right)$ et $GS{p}_4\left(F\right)$
3. Thomas J. Haines, Base change for Bernstein centers of depth zero principal series blocks
4. Laurent Clozel, Michael Harris, Richard Taylor, Automorphy for some l-adic lifts of automorphic mod l Galois representations
5. Thomas J. Haines, Michael Rapoport, Shimura varieties with ${\Gamma }_1\left(p\right)$-level via Hecke algebra isomorphisms: the Drinfeld case