Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations
Algebraic Geometry
2021-05-11 v3 Representation Theory
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 -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 -forms.
Keywords
Cite
@article{arxiv.1805.01664,
title = {Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations},
author = {Naoki Fujita and Eunjeong Lee and Dong Youp Suh},
journal= {arXiv preprint arXiv:1805.01664},
year = {2021}
}