Parabolic induction and Hecke modules in characteristic p for p-adic GLn

被引：18
|
作者：
Ollivier, Rachel [1 ]
机构：
[1] Univ Versailles St Quentin, Lab Math Versailles, F-78035 Versailles, France
来源：
ALGEBRA & NUMBER THEORY | 2010年 / 4卷 / 06期
关键词：
mod p representations of Hecke algebras and p-adic groups; parabolic induction; integral Bernstein presentation; integral Satake transform; PRINCIPAL SERIES; REPRESENTATIONS; GL(2)(F); ALGEBRA; IWAHORI;
D O I：
10.2140/ant.2010.4.701
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We classify the simple supersingular modules for the pro-p-Iwahori Hecke algebra H of p-adic GL(n) by proving a conjecture by Vigneras about a mod p numerical Langlands correspondence on the side of the Hecke modules. We define a process of induction for H-modules in characteristic p that reflects the parabolic induction for representations of the p-adic general linear group and explore the semisimplification of the standard nonsupersingular H-modules in light of this process.
引用
收藏
页码：701 / 742
页数：42
相关论文
共 50 条
  • [11] Estimates for p-adic valuations of Hecke operator eigenvalues
    Lafforgue, Vincent
    BULLETIN DE LA SOCIETE MATHEMATIQUE DE FRANCE, 2011, 139 (04): : 455 - 477
  • [12] The classification of irreducible admissible mod p representations of a p-adic GLn
    Herzig, Florian
    INVENTIONES MATHEMATICAE, 2011, 186 (02) : 373 - 434
  • [13] Affine quiver Schur algebras and p-adic GLn
    Miemietz, Vanessa
    Stroppel, Catharina
    SELECTA MATHEMATICA-NEW SERIES, 2019, 25 (02):
  • [14] Parameters of Hecke algebras for Bernstein components of p-adic groups
    Solleveld, Maarten
    INDAGATIONES MATHEMATICAE-NEW SERIES, 2025, 36 (01): : 124 - 170
  • [15] Iwahori-Hecke algebras for p-adic loop groups
    Braverman, Alexander
    Kazhdan, David
    Patnaik, Manish M.
    INVENTIONES MATHEMATICAE, 2016, 204 (02) : 347 - 442
  • [16] Parabolic induction in characteristic p
    Rachel Ollivier
    Marie-France Vignéras
    Selecta Mathematica, 2018, 24 : 3973 - 4039
  • [17] The pro-p-Iwahori Hecke algebra of a reductive p-adic group I
    Vigneras, Marie-France
    COMPOSITIO MATHEMATICA, 2016, 152 (04) : 693 - 753
  • [18] Parabolic induction in characteristic p
    Ollivier, Rachel
    Vigneras, Marie-France
    SELECTA MATHEMATICA-NEW SERIES, 2018, 24 (05): : 3973 - 4039
  • [19] (φ, Γ) -modules of de Rham and p-adic L functions
    Jacinto, Joaquin Rodrigues
    ALGEBRA & NUMBER THEORY, 2018, 12 (04) : 885 - 934
  • [20] Hecke algebras for p-adic reductive groups and Local Langlands Correspondences for Bernstein blocks
    Aubert, Anne-Marie
    Xu, Yujie
    ADVANCES IN MATHEMATICS, 2024, 436
12345