2003/01/07 by Marie‐France Vignéras, Marie-France Vigneras, Vigneras, Marie-France
Mathematics · #22E50 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:22E50
paper · pdf · doi:10.48550/arxiv.math/0301058
openalex publication_date 2003/01/07 · arxiv created 2004/07/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let H be a generic affine Hecke algebra (Iwahori-Matsumoto definition) over a polynomial algebra with a finite number of indeterminates over the ring of integers. We prove the existence of an integral Bernstein-Lusztig basis related to the Iwahori-Matsumoto basis by a strictly upper triangular matrix, from which we deduce that the center Z of H is finitely generated and that H is a finite type Z-module (this was proved after inversion of the parameters by Bernstein-Lusztig), and we give some applications to the theory of H-modules where the parameters act by 0. These results are related to the smooth p-adic or mod p representations of reductive p-adic groups. We introduce the supersingular modules of the affine Hecke algebra of GL(n) with parameter 0, probably analogues of the Barthel-Livne supersingular mod p representations of GL(2).