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