Littlewood--Richardson coefficients and integrable tilings
Abstract
Description
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.
29 pages, color figures. v2: corrected minor misprints and added short appendix. v3: fig 16 fixed
29 pages, color figures. v2: corrected minor misprints and added short appendix. v3: fig 16 fixed