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Published September 22, 2017 | Submitted
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Bounded Littlewood identities


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.

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.

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August 20, 2023
August 20, 2023