X=M for symmetric powers

Details X=M for symmetric powers X=M for symmetric powers

2004-12-19

arxiv.org/abs/math/0412376v2

J. Algebra 295 (2006) 562-610

Mathematics

Quantum Algebra

40 pages; to appear in J. Algebra

Scientific paper

10.1016/j.jalgebra.2005.04.023

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.

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