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BC_n-symmetric polynomials

Rains, Eric M. (2005) BC_n-symmetric polynomials. Transformation Groups, 10 (1). pp. 63-132. ISSN 1083-4362. doi:10.1007/s00031-005-1003-y.

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We consider two important families of BC_n-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.

Item Type:Article
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Additional Information:© 2005 Birkhauser Boston. Received: 03 October 2003; Accepted: 07 October 2004.
Issue or Number:1
Record Number:CaltechAUTHORS:20171002-161044221
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Official Citation:Rains, E. Transformation Groups (2005) 10: 63.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81978
Deposited By: Tony Diaz
Deposited On:02 Oct 2017 23:19
Last Modified:15 Nov 2021 19:47

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