Relative hard Lefschetz for Soergel bimodules

Abstract

We prove the relative hard Lefschetz theorem for Soergel bimodules. It follows that the structure constants of the Kazhdan-Lusztig basis are unimodal. We explain why the relative hard Lefschetz theorem implies that the tensor category associated by Lusztig to any 2-sided cell in a Coxeter group is rigid and pivotal.

29 pages, v2: added a missing assumption in Remark 5.1

References in corpus (2)

• Truncated convolution of character sheaves
• Multi-fusion categories of Harish-Chandra bimodules

Cited by in corpus (2)

• Simple transitive $2$-representations of Soergel bimodules for finite Coxeter types
• Actions of sl_2 on algebras appearing in categorification