Littlewood–Richardson coefficients and integrable tilings

Paul Zinn-Justin 1

The Electronic Journal of Combinatorics 16 (2009) R12

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.

  • 1. Laboratoire de Physique Théorique et Hautes Energies (LPTHE),
    CNRS : UMR7589 – Université Paris VI – Pierre et Marie Curie – Université Paris VII – Paris Diderot
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