Littlewood-Richardson coefficients and integrable tilings

Abstract

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.