Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some noncommutative algebras related to K-theory of flag varieties,
  part I   For any Lie algebra of classical type or type $G_2$ we define a $K$-theoretic
analog of Dunkl's elements, the so-called truncated {\it
Ruijsenaars-Schneider-Macdonald elements}, $RSM$-elements for short, in the
corresponding {\it Yang-Baxter group}, which form a commuting family of
elements in the latter. For the root systems of type $A$ we prove that the
subalgebra of the {\it bracket algebra} generated by the RSM-elements is
isomorphic to the Grothendieck ring of the flag variety. In general, we prove
that the subalgebra generated by the {\it images} of the RSM-elements in the
corresponding {\it Nichols-Woronowicz algebra} is canonically isomorphic to the
Grothendieck ring of the corresponding flag varieties of classical type or of
type $G_2$. In other words, we construct the ``Nichols-Woronowicz algebra
model'' for the Grothendieck Calculus on Weyl groups of classical type or type
$G_2,$ providing a partial generalization of some recent results by Y. Bazlov.
We also give a conjectural description (theorem for type $A$) of a commutative
subalgebra generated by the {\it truncated RSM-elements} in the bracket algebra
for the classical root systems. Our results provide a proof and generalizations
of recent conjecture and result by C. Lenart and A. Yong for the root system of
type $A$.

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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: q-fin
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an