Geodesic
Representations of affine Hecke algebras and based rings of affine Weyl groups
Xi, Nanhua1
1 Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China
Journal of the American Mathematical Society, Tome 20 (2007) no. 1, pp. 211-217

Voir la notice de l'article provenant de la source American Mathematical Society

In this paper we show that the Deligne-Langlands-Lusztig classification of simple representations of an affine Hecke algebra remains valid if the parameter is not a root of the corresponding Poincaré polynomial. This verifies a conjecture of Lusztig proposed in 1989.
DOI : 10.1090/S0894-0347-06-00539-X

Xi, Nanhua 1

1 Institute of Mathematics, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China 
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Xi, Nanhua. Representations of affine Hecke algebras and based rings of affine Weyl groups. Journal of the American Mathematical Society, Tome 20 (2007) no. 1, pp. 211-217. doi: 10.1090/S0894-0347-06-00539-X

[1] Ariki, Susumu, Mathas, Andrew The number of simple modules of the Hecke algebras of type 𝐺(𝑟,1,𝑛) Math. Z. 2000 601 623

[2] Bezrukavnikov, Roman, Ostrik, Viktor On tensor categories attached to cells in affine Weyl groups. II 2004 101 119

[3] Borel, Armand Admissible representations of a semi-simple group over a local field with vectors fixed under an Iwahori subgroup Invent. Math. 1976 233 259

[4] Grojnowski, I. Representations of affine Hecke algebras (and affine quantum 𝐺𝐿_{𝑛}) at roots of unity Internat. Math. Res. Notices 1994

[5] Gyoja, Akihiko Modular representation theory over a ring of higher dimension with applications to Hecke algebras J. Algebra 1995 553 572

[6] Gyoja, Akihiko Cells and modular representations of Hecke algebras Osaka J. Math. 1996 307 341

[7] Kazhdan, David, Lusztig, George Representations of Coxeter groups and Hecke algebras Invent. Math. 1979 165 184

[8] Kazhdan, David, Lusztig, George Proof of the Deligne-Langlands conjecture for Hecke algebras Invent. Math. 1987 153 215

[9] Lusztig, George Singularities, character formulas, and a 𝑞-analog of weight multiplicities 1983 208 229

[10] Lusztig, George Cells in affine Weyl groups 1985 255 287

[11] Lusztig, George Cells in affine Weyl groups. II J. Algebra 1987 536 548

[12] Lusztig, George Cells in affine Weyl groups. II J. Algebra 1987 536 548

[13] Lusztig, George Cells in affine Weyl groups. IV J. Fac. Sci. Univ. Tokyo Sect. IA Math. 1989 297 328

[14] Lusztig, George Representations of affine Hecke algebras Astérisque 1989 73 84

[15] Vignã©Ras, Marie-France Modular representations of 𝑝-adic groups and of affine Hecke algebras 2002 667 677

[16] Xi, Nan Hua Representations of affine Hecke algebras 1994

[17] Xi, Nanhua The based ring of two-sided cells of affine Weyl groups of type ̃𝐴_{𝑛-1} Mem. Amer. Math. Soc. 2002

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