Littlewood--Richardson coefficients and integrable tilings

Details Littlewood--Richardson coefficients and integrable tilings Littlewood--Richardson coefficients and integrable tilings

2008-09-14

arxiv.org/abs/0809.2392v4

Physics

Mathematical Physics

29 pages, color figures. v2: corrected minor misprints and added short appendix. v3: fig 16 fixed

Scientific paper

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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