Evaluation birepresentations of affine type A Soergel bimodules

Marco Mackaay, Vanessa Miemietz, Pedro Vaz

Research output: Contribution to journalArticlepeer-review

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.
Original languageEnglish
Article number109401
JournalAdvances in Mathematics
Volume436
Early online date21 Nov 2023
DOIs
Publication statusPublished - Jan 2024

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