Affine quiver Schur algebras and p-adic $${\textit{GL}}_n$$ GL n
| Autor: | Vanessa Miemietz, Catharina Stroppel |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Hecke algebra
Pure mathematics Endomorphism General Mathematics 010102 general mathematics Quiver General Physics and Astronomy General linear group Field (mathematics) Basis (universal algebra) Unipotent Schur algebra 01 natural sciences 0101 mathematics Mathematics::Representation Theory Mathematics |
| Zdroj: | Selecta Mathematica. 25 |
| ISSN: | 1420-9020 1022-1824 |
| DOI: | 10.1007/s00029-019-0474-y |
| Popis: | In this paper we consider the (affine) Schur algebra which arises as the endomorphism algebra of certain permutation modules for the Iwahori–Matsumoto Hecke algebra. This algebra describes, for a general linear group over a p-adic field, a large part of the unipotent block over fields of characteristic different from p. We show that this Schur algebra is, after a suitable completion, isomorphic to the quiver Schur algebra attached to the cyclic quiver. The isomorphism is explicit, but nontrivial. As a consequence, the completed (affine) Schur algebra inherits a grading. As a byproduct we obtain a detailed description of the algebra with a basis adapted to the geometric basis of quiver Schur algebras. We illustrate the grading in the explicit example of $${\text {GL}}_2({\mathbb {Q}}_5)$$ in characteristic 3. |
| Databáze: | OpenAIRE |
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