Algebraic and geometric properties of flag Bott–Samelson varieties and applications to representations

Abstract

We define and study flag Bott-Samelson varieties which generalize both Bott-Samelson varieties and flag varieties.Using a birational morphism from an appropriate Bott-Samelson variety to a flag Bott-Samelson variety, we compute the Newton-Okounkov bodies of flag Bott-Samelson varieties as generalized string polytopes, which are applied to give polyhedral expressions for irreducible decompositions of tensor products of G-modules.Furthermore, we show that flag Bott-Samelson varieties degenerate into flag Bott manifolds with higher rank torus actions, and we describe the Duistermaat-Heckman measures of the moment map images of flag Bott-Samelson varieties with torus actions and invariant closed 2-forms.

Locations

• Pacific Journal of Mathematics - View
• arXiv (Cornell University) - View - PDF
• DataCite API - View