Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quadratic transformations of Macdonald and Koornwinder polynomials   When one expands a Schur function in terms of the irreducible characters of
the symplectic (or orthogonal) group, the coefficient of the trivial character
is 0 unless the indexing partition has an appropriate form. A number of
q-analogues of this fact were conjectured in math.QA/0112035; the present paper
proves most of those conjectures, as well as some new identities suggested by
the proof technique. The proof involves showing that a nonsymmetric version of
the relevant integral is annihilated by a suitable ideal of the affine Hecke
algebra, and that any such annihilated functional satisfies the desired
vanishing property. This does not, however, give rise to vanishing identities
for the standard nonsymmetric Macdonald and Koornwinder polynomials; we discuss
the required modification to these polynomials to support such results.

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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: physics
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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: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-ph