Hecke algebra with respect to the pro-p-radical of a maximal compact open subgroup for GL(n,F) and its inner forms
| Autor: | Gianmarco Chinello |
|---|---|
| Přispěvatelé: | Chinello, G |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Inner forms of p-adic general linear group
Hecke algebra Level 0 representation Presentation by generators and relation Commutative ring 01 natural sciences Unitary state modular representations p-adic group Combinatorics modular representation 0103 physical sciences FOS: Mathematics Algebra di Hecke gruppi p-adici rappresentazioni modulari blocchi di livello 0 Hecke algebra p-adic groups modular representations level-0 blocks Locally compact space 0101 mathematics Representation Theory (math.RT) Direct product Mathematics gruppi p-adici p-adic groups Subcategory 20C08 Algebra and Number Theory blocchi di livello 0 010102 general mathematics Mathematics - Rings and Algebras MAT/02 - ALGEBRA Rings and Algebras (math.RA) Category of modules Coset Modular representations of p-adic reductive group 010307 mathematical physics Algebra di Hecke level-0 blocks Mathematics - Representation Theory rappresentazioni modulari |
| Popis: | Let $G$ be a direct product of inner forms of general linear groups over non-archimedean locally compact fields of residue characteristic $p$ and let $K^1$ be the pro-$p$-radical of a maximal compact open subgroup of $G$. In this paper we describe the (intertwining) Hecke algebra $\mathscr{H}(G,K^1)$, that is the convolution $\mathbb{Z}$-algebra of functions from $G$ to $\mathbb{Z}$ that are bi-invariant for $K^1$ and whose supports are a finite union of $K^1$-double cosets. We produce a presentation by generators and relations of this algebra. Finally we prove that the level-$0$ subcategory of the category of smooth representations of $G$ over a unitary commutative ring $R$ such that $p\in R^{\times}$ is equivalent to the category of modules over $\mathscr{H}(G,K^1)\otimes_\mathbb{Z} R$. Comment: 17 pages, minor corrections, updated bibliography |
| Databáze: | OpenAIRE |
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