JournalsjemsVol. 23, No. 8pp. 2549–2581

Relative hard Lefschetz for Soergel bimodules

  • Ben Elias

    University of Oregon, Eugene, USA

  • Geordie Williamson

    University of Sydney, Australia
Relative hard Lefschetz for Soergel bimodules cover
Download PDF

This article is published open access under our Subscribe to Open model.

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 two-sided cell in a Coxeter group is rigid and pivotal.

Cite this article

Ben Elias, Geordie Williamson, Relative hard Lefschetz for Soergel bimodules. J. Eur. Math. Soc. 23 (2021), no. 8, pp. 2549–2581

DOI 10.4171/JEMS/1061