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