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Mathematics > Algebraic Geometry

arXiv:1805.01664 (math)
[Submitted on 4 May 2018 (v1), last revised 14 Apr 2020 (this version, v3)]

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

Authors: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.
Subjects: Algebraic Geometry (math.AG); Representation Theory (math.RT)
MSC classes: Primary: 05E10, Secondary: 14M15, 57S25
Report number: MR4202007
Cite as: arXiv:1805.01664 [math.AG]
  (or arXiv:1805.01664v3 [math.AG] for this version)
  https://doi.org/10.48550/arXiv.1805.01664
Journal reference: Pacific J. Math. 309 (2020) 145-194
Related DOI: https://doi.org/10.2140/pjm.2020.309.145

Submission history

From: Eunjeong Lee [view email]
[v1] Fri, 4 May 2018 08:47:08 UTC (36 KB)
[v2] Thu, 14 Mar 2019 09:24:24 UTC (38 KB)
[v3] Tue, 14 Apr 2020 02:52:26 UTC (43 KB)
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