Evaluation birepresentations of affine type a soergel bimodules

Mackaay, Marco; Miemietz, Vanessa; Vaz, Pedro

http://hdl.handle.net/10400.1/20536

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Autores

Mackaay, Marco

Miemietz, Vanessa

Vaz, Pedro

Resumo(s)

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. (c) 2023 Elsevier Inc. All rights reserved.