Relative hard Lefschetz for Soergel bimodules
Representation Theory
2017-11-13 v2 Algebraic Geometry
Quantum Algebra
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.
Cite
@article{arxiv.1607.03271,
title = {Relative hard Lefschetz for Soergel bimodules},
author = {Ben Elias and Geordie Williamson},
journal= {arXiv preprint arXiv:1607.03271},
year = {2017}
}
Comments
29 pages, v2: added a missing assumption in Remark 5.1