Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Geometric and unipotent crystals II: From unipotent bicrystals to
  crystal bases   For each reductive algebraic group G we introduce and study unipotent
bicrystals which serve as a regular version of birational geometric and
unipotent crystals introduced earlier by the authors.
  The framework of unipotent bicrystals allows, on the one hand, to study
systematically such varieties as Bruhat cells in G and their convolution
products and, on the other hand, to give a new construction of many normal
Kashiwara crystals including those for G^\vee-modules, where G^\vee is the
Langlands dual groups. In fact, our analogues of crystal bases (which we refer
to as crystals associated to G^\vee-modules) are associated to G^\vee-modules
directly, i.e., without quantum deformations.
  One of the main results of the present paper is an explicit construction of
the crystal B_0 for the coordinate ring of the (Langlands dual) flag variety
based on the positive unipotent bicrystal on the open Bruhat cell.
  Our general tropicalization procedure assigns to each strongly positive
unipotent bicrystal a normal Kashiwara crystal B equipped with the multiplicity
erasing homomorphism B--> B_0 and the combinatorial central charge B--> Z which
is invariant under all crystal operators.

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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg