Bounded Littlewood identities for cylindric Schur functions

Abstract

The identities which are in the literature often called ``bounded Littlewood identities" are determinantal formulas for the sum of Schur functions indexed by partitions with bounded height. They have interesting combinatorial consequences such as connections between standard Young tableaux of bounded height, lattice walks in a Weyl chamber, and noncrossing matchings. In this paper we prove affine analogs of the bounded Littlewood identities. These are determinantal formulas for sums of cylindric Schur functions. We also study combinatorial aspects of these identities. As a consequence we obtain an unexpected connection between cylindric standard Young tableaux and \( r \)-noncrossing and \( s \)-nonnesting matchings.