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Bounded Littlewood identities

Rains, Eric M. and Warnaar, S. Ole (2015) Bounded Littlewood identities. . (Submitted)

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We describe a method, based on the theory of Macdonald-Koornwinder polynomials, for proving bounded Littlewood identities. Our approach provides an alternative to Macdonald's partial fraction technique and results in the first examples of bounded Littlewood identities for Macdonald polynomials. These identities, which take the form of decomposition formulas for Macdonald polynomials of type (R,S) in terms Macdonald polynomials of type A, are q,t-analogues of known branching formulas for characters of the symplectic, orthogonal and special orthogonal groups, important in the theory of plane partitions. As applications of our results we obtain combinatorial formulas for characters of affine Lie algebras, Rogers-Ramanujan identities for such algebras complementing recent results of Griffin et al., and transformation formulas for Kaneko-Macdonald-type hypergeometric series.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Paper
Warnaar, S. Ole0000-0002-9786-0175
Additional Information:Work supported by the National Science Foundation (grant number DMS-1001645) and the Australian Research Council. We thank Michael Schlosser, Hjalmar Rosengren and Jasper Stokman for helpful discussions on hypergeometric function, Macdonald identities and Macdonald–Koornwinder polynomials. We thank Richard Stanley for pointing out the paper [86] by Schur.
Funding AgencyGrant Number
Australian Research CouncilUNSPECIFIED
Classification Code:2010 Mathematics Subject Classification: 05E05, 05E10, 17B67, 33D67
Record Number:CaltechAUTHORS:20170922-141021522
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:81762
Deposited By: Tony Diaz
Deposited On:22 Sep 2017 21:23
Last Modified:03 Oct 2019 18:46

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