JiSun Huh, Jang Soo Kim, Christian Krattenthaler and Soichi Okada

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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