Local Hodge theory of Soergel bimodules

Abstract

We prove the local hard Lefschetz theorem and local Hodge-Riemann bilinear relations for Soergel bimodules. Using results of Soergel and Kübel one may deduce an algebraic proof of the Jantzen conjectures. We observe that the Jantzen filtration may depend on the choice of non-dominant regular deformation direction.

arXiv comment54 pages, v3: further minor changes. Final version to appear in Acta. Math