Bounded Littlewood identities

摘要: 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 first examples identities Macdonald polynomials. These identities, which take form decomposition formulas polynomials type $(R,S)$ terms ordinary are $q,t$-analogues known branching characters symplectic, orthogonal special groups. In classical limit, our method implies that MacMahon's famous ex-conjecture generating function symmetric plane partitions box follows from identification $(\mathrm{GL}(n,\mathbb{R}),\mathrm{O}(n))$ as Gelfand pair. As further applications, we obtain combinatorial affine Lie algebras; Rogers-Ramanujan algebras, complementing recent Griffin et al.; quadratic transformation Kaneko--Macdonald-type basic hypergeometric series.