Abstract
In this paper we consider the (affine) Schur algebra which arises as the endomorphism algebra of certain permutation modules for the IwahoriMatsumoto Hecke algebra. This algebra describes, for a general linear group over a padic 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 language  English 

Article number  32 
Journal  Selecta MathematicaNew Series 
Volume  25 
Early online date  16 Apr 2019 
DOIs  
Publication status  Published  Jun 2019 
Profiles

Vanessa Miemietz
 School of Mathematics  Associate Professor in Pure Mathematics
 Algebra and Combinatorics  Member
Person: Research Group Member, Academic, Teaching & Research