Types and Hecke algebras for principal series representations of split reductive p-adic groups
Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 31 (1998) no. 3, p. 361-413
@article{ASENS_1998_4_31_3_361_0,
     author = {Roche, Alan},
     title = {Types and Hecke algebras for principal series representations of split reductive $p$-adic groups},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Elsevier},
     volume = {Ser. 4, 31},
     number = {3},
     year = {1998},
     pages = {361-413},
     doi = {10.1016/s0012-9593(98)80139-0},
     zbl = {0903.22009},
     mrnumber = {99d:22028},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_1998_4_31_3_361_0}
}
Roche, Alan. Types and Hecke algebras for principal series representations of split reductive $p$-adic groups. Annales scientifiques de l'École Normale Supérieure, Série 4, Volume 31 (1998) no. 3, pp. 361-413. doi : 10.1016/s0012-9593(98)80139-0. http://www.numdam.org/item/ASENS_1998_4_31_3_361_0/

[1] J. D. Adler, Refined anisotropic K-types and supercuspidal representations. Pacific Journal of Mathematics, to appear. | Zbl 0924.22015

[2] J. D. Adler and A. Roche, An intertwining result for p-adic groups. Preprint.

[3] H. Bass, Algebraic K-Theory, New York, 1968. | MR 40 #2736 | Zbl 0174.30302

[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). | MR 86e:22028 | Zbl 0599.22016

[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). | Numdam | MR 58 #28310 | Zbl 0412.22015

[6] A. Borel, Admissible representations of a semisimple group with vectors fixed under an Iwahori subgroup (Invent. Math., Vol. 35, 1976, pp. 233-259). | MR 56 #3196 | Zbl 0334.22012

[7] N. Bourbaki, Groupes et Algèbres de Lie. Chap. IV, V, VI. Hermann, 1968.

[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). | Numdam | MR 48 #6265 | Zbl 0254.14017

[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). | Numdam | Zbl 0597.14041

[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. | MR 94h:22007 | Zbl 0787.22016

[11] C. J. Bushnell and P. C. Kutzko, Semisimple types for GL(N). Preprint.

[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). | Numdam | MR 94a:22033 | Zbl 0787.22017

[13] C. J. Bushnell and P. C. Kutzko, Smooth representations of reductive p-adic groups : structure theory via types. Preprint, February 1996.

[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. | MR 81e:22029 | Zbl 0421.22010

[15] W. Casselman, The unramified principal series of p-adic groups I (Comp. Math., Vol. 40, 1980, pp. 387-406). | Numdam | MR 83a:22018 | Zbl 0472.22004

[16] F. Digne and J. Michel, Representations of finite groups of Lie type. Cambridge University Press, 1991. | MR 92g:20063 | Zbl 0815.20014

[17] D. Goldstein, Hecke algebra isomorphisms for tamely ramified characters. Ph.D. thesis, University of Chicago, 1990.

[18] R. B. Howlett and G. I. Lehrer, Induced cuspidal representations and generalised Hecke rings (Inv. Math., Vol. 58, 1980, pp. 37-64). | MR 81j:20017 | Zbl 0435.20023

[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. | MR 87h:22023 | Zbl 0593.22014

[20] R. Howe, Principal series of GLn over p-adic fields (Trans. Am. Math. Soc., Vol. 177, 1973, pp. 275-286). | MR 48 #6324 | Zbl 0257.22018

[21] J. E. Humphreys, Linear Algebraic Groups. Springer-Verlag, New York, 1975. | MR 53 #633 | Zbl 0325.20039

[22] J. E. Humphreys, Reflection groups and Coxeter groups. Cambridge University Press, 1990. | MR 92h:20002 | Zbl 0725.20028

[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). | Numdam | MR 32 #2486 | Zbl 0228.20015

[24] D. Kazhdan and G. Lusztig, Proof of the Deligne-Langlands conjecture for Hecke algebras (Invent. Math., Vol. 87, 1987, pp. 153-215). | MR 88d:11121 | Zbl 0613.22004

[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. | MR 91e:22017 | Zbl 0741.22009

[26] G. Lusztig, Classification of unipotent representations of simple p-adic groups (Internat. Math. Res. Notices No. 11, 1995, pp. 517-589). | MR 98b:22034 | Zbl 0872.20041

[27] L. E. Morris, Tamely ramified intertwining algebras (Invent. Math., Vol. 114, 1993, pp. 1-54). | MR 94g:22035 | Zbl 0854.22022

[28] L. E. Morris, Level zero G-types. Preprint, 1994.

[29] A. Moy and G. Prasad, Jacquet functors and unrefined minimal K-types (Comm. Math. Helv., Vol. 71, 1996, pp. 98-121). | MR 97c:22021 | Zbl 0860.22006

[30] M. Reeder, Nonstandard intertwining operators and the structure of unramified principal series representations (Forum. Math., Vol. 9, no. 4, 1997, pp. 457-516). | MR 98j:22028 | Zbl 0882.22020

[31] G. Sanje-Mpacko, Ph.D. thesis, Rutgers University, 1994.

[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. | MR 80h:20062 | Zbl 0416.20034

[33] T. A. Springer and R. Steinberg, Conjugacy Classes (Lecture Notes in Math., Vol. 131, Springer-Verlag, Berlin, 1970, pp. 167-266). | MR 42 #3091 | Zbl 0249.20024

[34] R. Steinberg, Endomorphisms of linear algebraic groups (Mem. Amer. Math. Soc., No. 80, 1968). | MR 37 #6288 | Zbl 0164.02902

[35] R. Steinberg, Torsion in reductive groups (Adv. Math., Vol. 15, 1975, pp. 63-92). | MR 50 #7369 | Zbl 0312.20026

[36] M. Tadic, Representations of p-adic symplectic groups (Comp. Math., Vol. 90, 1994, pp. 123-181). | Numdam | MR 95a:22025 | Zbl 0797.22008