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.