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Affine quiver Schur algebras and p-adic GLn

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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.

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Original languageEnglish
Article number32
JournalSelecta Mathematica
Volume25
Early online date16 Apr 2019
DOIs
Publication statusPublished - Jun 2019
Peer-reviewedYes

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ID: 150569649

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