Evaluation birepresentations of affine type A Soergel bimodules
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.
Cite
@article{arxiv.2207.02459,
title = {Evaluation birepresentations of affine type A Soergel bimodules},
author = {M. Mackaay and V. Miemietz and P. Vaz},
journal= {arXiv preprint arXiv:2207.02459},
year = {2023}
}
Comments
61 pages, lots of colored pictures. v2, accepted version