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arXiv · 1805.01664

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

Naoki Fujita·Eunjeong Lee·Dong Youp Suh
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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.

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Naoki Fujita, Eunjeong Lee, Dong Youp Suh. 2018-05-04. Algebraic and geometric properties of flag Bott-Samelson varieties and applications to representations. https://doi.org/10.2140/pjm.2020.309.145

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