The N\'eron-Severi Lie Algebra of a Soergel Module
Representation Theory
2017-01-06 v2
Abstract
We introduce the N\'eron-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 N\'eron-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 Poincar\'e duality.
Keywords
Cite
@article{arxiv.1607.05565,
title = {The N\'eron-Severi Lie Algebra of a Soergel Module},
author = {Leonardo Patimo},
journal= {arXiv preprint arXiv:1607.05565},
year = {2017}
}
Comments
25 pages, major revision, proofs have more details, added appendix on the case of general Coxeter groups