X=M for symmetric powers
Quantum Algebra
2007-05-23 v2 Combinatorics
Abstract
The X=M conjecture of Hatayama et al. asserts the equality between the one-dimensional configuration sum X expressed as the generating function of crystal paths with energy statistics and the fermionic formula M for all affine Kac--Moody algebra. In this paper we prove the X=M conjecture for tensor products of Kirillov--Reshetikhin crystals B^{1,s} associated to symmetric powers for all nonexceptional affine algebras.
Keywords
Cite
@article{arxiv.math/0412376,
title = {X=M for symmetric powers},
author = {Anne Schilling and Mark Shimozono},
journal= {arXiv preprint arXiv:math/0412376},
year = {2007}
}
Comments
40 pages; to appear in J. Algebra