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

Abstract

We introduce the notion of flag Bott-Samelson variety as a generalization of Bott-Samelson variety and flag variety. Using a birational morphism from an appropriate Bott-Samelson variety to a flag Bott-Samelson variety, we compute 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 are degenerated into flag Bott manifolds with higher rank torus actions, and find the Duistermaat-Heckman measures of the moment map images of flag Bott-Samelson varieties with the torus action together with invariant closed $2$-forms.

References in corpus (5)

• Rhombic tilings and Bott-Samelson varieties
• Flag Bott manifolds and the toric closure of a generic orbit associated to a generalized Bott manifold
• Flag Bott manifolds of general Lie type and their equivariant cohomology rings
• Some combinatorial aspects of generalised Bott-Samelson varieties
• Grossberg-Karshon twisted cubes and hesitant jumping walk avoidance

Cited by in corpus (5)

• Flag Bott manifolds and the toric closure of a generic orbit associated to a generalized Bott manifold
• Flag Bott manifolds of general Lie type and their equivariant cohomology rings
• On Schubert varieties of complexity one
• Equivariant $K$-theory of flag Bott manifolds of general Lie type
• $K$-theory of Flag Bott manifolds