The Néron-Severi Lie Algebra of a Soergel Module

2016/07/19 by Patimo, Leonardo
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1607.05565

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.

Related

• A diagram algebra for Soergel modules corresponding to smooth Schubert varieties
• Neron-Severi Lie algebra, autoequivalences of the derived category, and monodromy
• B-sub-modules of Lie(G)/Lie(B) and Smooth Schubert Varieties in G/B
• La théorie de Hodge des bimodules de Soergel (d'après Soergel et Elias-Williamson)
• Soergel calculus and Schubert calculus