Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integrality of two variable Kostka functions   The two variable Kostka functions are the scalar products of the Macdonald
polynomials with the Schur polynomials with respect to the scalar product which
makes the Hall-Littlewood polynomials pairwise orthogonal. A conjecture of
Macdonald states that they are polynomials in q and t with non-negative
integral coefficients. We prove that the Kostka functions are at least
polynomials with integral coefficients. The main idea is to prove an analogous
statement for the non-symmetric Macdonald polynomials by establishing recursion
relations via the affine Hecke algebra.

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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: nlin
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The categories of this paper are: supr-con