Tensor categories attached to exceptional cells in Weyl groups

TL;DR

This paper identifies a specific monoidal category associated with a two-sided cell in a Weyl group, advancing the understanding of tensor categories linked to algebraic structures in representation theory.

Contribution

It determines the structure of the tensor category attached to an exceptional two-sided cell in Weyl groups, completing previous classifications.

Findings

Explicit identification of the monoidal category for the exceptional cell

Extension of Lusztig's framework to new cases

Enhanced understanding of cell-related tensor categories

Abstract

Using truncated convolution of perverse sheaves on a flag variety Lusztig associated a monoidal category to a two sided cell in the Weyl group. We identify this category in the case which was not decided previously.