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arXiv · 2207.02459

Evaluation birepresentations of affine type A Soergel bimodules

M. Mackaay·V. Miemietz·P. Vaz
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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.

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BibTeXRIS

M. Mackaay, V. Miemietz, P. Vaz. 2022-07-06. Evaluation birepresentations of affine type A Soergel bimodules. https://arxiv.org/abs/2207.02459

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