Littlewood--Richardson coefficients and integrable tilings
Mathematical Physics
2009-01-16 v4 Combinatorics
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.0809.2392,
title = {Littlewood--Richardson coefficients and integrable tilings},
author = {P. Zinn-Justin},
journal= {arXiv preprint arXiv:0809.2392},
year = {2009}
}
Comments
29 pages, color figures. v2: corrected minor misprints and added short appendix. v3: fig 16 fixed