Affine quiver Schur algebras and p-adic GLn

Miemietz, Vanessa and Stroppel, Catharina (2019) Affine quiver Schur algebras and p-adic GLn. Selecta Mathematica-New Series, 25. ISSN 1022-1824

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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.

Item Type:	Article
Faculty \ School:	Faculty of Science > School of Mathematics (former - to 2024)
UEA Research Groups:	Faculty of Science > Research Groups > Algebra and Combinatorics (former - to 2024) Faculty of Science > Research Groups > Algebra, Number Theory, Logic, and Representations (ANTLR)
Depositing User:	LivePure Connector
Date Deposited:	05 Feb 2019 09:30
Last Modified:	28 Oct 2025 00:51
URI:	https://ueaeprints.uea.ac.uk/id/eprint/69844
DOI:	10.1007/s00029-019-0474-y

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