ALGEBRAIC AND GEOMETRIC PROPERTIES OF FLAG BOTT-SAMELSON VARIETIES AND APPLICATIONS TO REPRESENTATIONS

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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.
Publisher
PACIFIC JOURNAL MATHEMATICS
Issue Date
2020-11
Language
English
Article Type
Article
Citation

PACIFIC JOURNAL OF MATHEMATICS, v.309, no.1, pp.145 - 194

ISSN
0030-8730
DOI
10.2140/pjm.2020.309.145
URI
http://hdl.handle.net/10203/280731
Appears in Collection
MA-Journal Papers(저널논문)
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