Evaluation birepresentations of affine type A Soergel bimodules

Mackaay, Marco, Miemietz, Vanessa and Vaz, Pedro (2024) Evaluation birepresentations of affine type A Soergel bimodules. Advances in Mathematics, 436. ISSN 0001-8708

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Abstract

In this paper, we use Soergel calculus to define a monoidal functor, called the evaluation functor, from extended affine type A Soergel bimodules to the homotopy category of bounded complexes in finite type A Soergel bimodules. This functor categorifies the well-known evaluation homomorphism from the extended affine type A Hecke algebra to the finite type A Hecke algebra. Through it, one can pull back the triangulated birepresentation induced by any finitary birepresentation of finite type A Soergel bimodules to obtain a triangulated birepresentation of extended affine type A Soergel bimodules. We show that if the initial finitary birepresentation in finite type A is a cell birepresentation, the evaluation birepresentation in extended affine type A has a finitary cover, which we illustrate by working out the case of cell birepresentations with subregular apex in detail.

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, Logic & Number Theory
Depositing User:	LivePure Connector
Date Deposited:	07 Nov 2023 02:49
Last Modified:	22 Nov 2024 01:38
URI:	https://ueaeprints.uea.ac.uk/id/eprint/93582
DOI:	10.1016/j.aim.2023.109401

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