Geodesic
Representations of affine Hecke algebras and based rings of affine Weyl groups
Xi, Nanhua1
1Institute 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 
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
@article{10_1090_S0894_0347_06_00539_X,
     author = {Xi, Nanhua},
     title = {Representations of affine {Hecke} algebras and based rings of affine {Weyl} groups},
     journal = {Journal of the American Mathematical Society},
     pages = {211--217},
     year = {2007},
     volume = {20},
     number = {1},
     doi = {10.1090/S0894-0347-06-00539-X},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-06-00539-X/}
}
TY  - JOUR
AU  - Xi, Nanhua
TI  - Representations of affine Hecke algebras and based rings of affine Weyl groups
JO  - Journal of the American Mathematical Society
PY  - 2007
SP  - 211
EP  - 217
VL  - 20
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-06-00539-X/
DO  - 10.1090/S0894-0347-06-00539-X
ID  - 10_1090_S0894_0347_06_00539_X
ER  - 
%0 Journal Article
%A Xi, Nanhua
%T Representations of affine Hecke algebras and based rings of affine Weyl groups
%J Journal of the American Mathematical Society
%D 2007
%P 211-217
%V 20
%N 1
%U http://geodesic.mathdoc.fr/articles/10.1090/S0894-0347-06-00539-X/
%R 10.1090/S0894-0347-06-00539-X
%F 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] Vignéras, 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

Cité par Sources :