Jucys-Murphy elements for Soergel bimodules

TL;DR

This paper introduces Jucys-Murphy elements for the diagrammatic category of Soergel bimodules in general Coxeter groups, enabling diagonalization of bilinear forms and deriving formulas for determinants and sums.

Contribution

It constructs Jucys-Murphy elements in a new categorical setting and applies them to analyze bilinear forms on cell modules.

Findings

Diagonalization of bilinear forms on cell modules

Explicit formulas for determinants of forms

Jantzen type sum formulas derived

Abstract

We produce Jucys-Murphy elements for the diagrammatical category of Soergel bimodules associated with general Coxeter groups, and use them to diagonalize the bilinear form on the cell modules. This gives rise to an expression for the determinant of the forms and Jantzen type sum formulas.