BCn-symmetric polynomials |
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Authors: | Eric M Rains |
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Institution: | (1) AT&T Labs-Research; Presently at Department of Mathematics, University of California, Davis, USA |
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Abstract: | We consider two important families of BCn-symmetric polynomials, namely Okounkov's
interpolation polynomials and Koornwinder's orthogonal
polynomials. We give a family of difference equations
satisfied by the former as well as generalizations of the
branching rule and Pieri identity, leading to a number of
multivariate q-analogues of classical hypergeometric
transformations. For the latter, we give new proofs of
Macdonald's conjectures, as well as new identities,
including an inverse binomial formula and several branching
rule and connection coefficient identities. We also derive
families of ordinary symmetric functions that reduce to the
interpolation and Koornwinder polynomials upon appropriate
specialization. As an application, we consider a number
of new integral conjectures associated to classical
symmetric spaces. |
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Keywords: | |
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