Littlewood--Richardson coefficients and integrable tilings

Paul Zinn-Justin (1)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies

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.

Domaines: Physique mathématique [math-ph]; Physique mathématique [math-ph]; Combinatoire [math.CO]

Paul Zinn-Justin. Littlewood--Richardson coefficients and integrable tilings. The Electronic Journal of Combinatorics, 2009, 16, pp.R12. ⟨hal-00370804⟩