The Néron-Severi Lie Algebra of a Soergel Module

Abstract

We introduce the Néron-Severi Lie algebra of a Soergel module and we determine it for a large class of Schubert varieties. This is achieved by investigating which Soergel modules admit a tensor decomposition. We also use the Néron-Severi Lie algebra to provide an easy proof of the well-known fact that a Schubert variety is rationally smooth if and only if its Betti numbers satisfy Poincaré duality.

arXiv comment25 pages, major revision, proofs have more details, added appendix on the case of general Coxeter groups