Affine quiver Schur algebras and p-adic GLn

Vanessa Miemietz, Catharina Stroppel

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Abstract

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 GL2(Q5) in characteristic 3.
Original languageEnglish
Article number32
JournalSelecta Mathematica
Volume25
Early online date16 Apr 2019
DOIs
Publication statusPublished - Jun 2019

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