Jucys-Murphy elements for Soergel bimodules

preprint2020arXivOpen access

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.

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