Braid group actions from categorical symmetric Howe duality on deformed Webster algebras

TL;DR

This paper constructs a 2-representation that categorifies a symmetric Howe representation of rak{gl}_m, leading to a categorical braid group action within a homotopy category.

Contribution

It introduces a deformation of Webster's algebra to realize a 2-representation of the symmetric Howe duality, establishing a new categorical braid group action.

Findings

Categorification of the symmetric Howe representation of rak{gl}_m.

Construction of a categorical braid group action.

Development of a deformed Webster algebra.

Abstract

We construct a 2-representation categorifying the symmetric Howe representation of $\mathfrak{gl}_m$ using a deformation of an algebra introduced by Webster. As a consequence, we obtain a categorical braid group action taking values in a homotopy category.