#### Vol. 309, No. 1, 2020

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

### Naoki Fujita, Eunjeong Lee and Dong Youp Suh

Vol. 309 (2020), No. 1, 145–194
DOI: 10.2140/pjm.2020.309.145
##### 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.

##### Keywords
flag Bott–Samelson varieties, Bott–Samelson varieties, Newton–Okounkov bodies, flag Bott manifolds
##### Mathematical Subject Classification
Primary: 05E10
Secondary: 14M15, 57S25
##### Milestones
Received: 14 July 2019
Revised: 13 April 2020
Accepted: 26 August 2020
Published: 26 December 2020
##### Authors
 Naoki Fujita Graduate School of Mathematical Sciences The University of Tokyo Meguro-ku Tokyo Japan Eunjeong Lee Center for Geometry and Physics Institute for Basic Science Pohang Republic of Korea Dong Youp Suh Department of Mathematical Sciences KAIST Yuseong-gu Daejeon Republic of Korea