The Hodge theory of Soergel bimodules

Abstract

We prove Soergel’s conjecture on the characters of indecomposable
Soergel bimodules. We deduce that Kazhdan-Lusztig polynomials have positive coefficients for arbitrary Coxeter systems. Using results of Soergel one may deduce an algebraic proof of the Kazhdan-Lusztig conjecture.

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Authors

Ben Elias

Massachusetts Institute of Technology, Cambridge, MA

Geordie Williamson

Max-Planck-Institut für Mathematik, Bonn, Germany