# Bounded Littlewood identities for cylindric Schur functions

### (42 pages)

**Abstract.**
The Gordon-Bender-Knuth identities are determinant formulas for the
sum of Schur functions of partitions with bounded height, which 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 an affine
analog of the Gordon-Bender-Knuth identities, which are determinant
formulas for the sum 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.

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