Littlewood–Richardson Coefficients and Integrable Tilings

Paul Zinn-Justin


We provide direct proofs of product and coproduct formulae for Schur functions where the coefficients (Littlewood–Richardson coefficients) are defined as counting puzzles. The product formula includes a second alphabet for the Schur functions, allowing in particular to recover formulae of [Molev–Sagan '99] and [Knutson–Tao '03] for factorial Schur functions. The method is based on the quantum integrability of the underlying tiling model.

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