Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algebraic and geometric properties of flag Bott-Samelson varieties and
  applications to representations   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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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: supr-con
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
0
The categories of this paper are: hep-ph
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The categories of this paper are: funct-an