Bounded Littlewood identities

Abstract

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.