2001/11/30 by Masato Okado, Anne Schilling, Mark Shimozono
Mathematics · #math.QA #math.CO #msc:17B67
published as Journal of Algebra 267 (2003) 212-245 · 27 pages; error corrected
arxiv created 2002/12/18 · arxiv updated 2009/11/30
Kang et al. provided a path realization of the crystal graph of a highest weight module over a quantum affine algebra, as certain semi-infinite tensor products of a single perfect crystal. In this paper, this result is generalized to give a realization of the tensor product of several highest weight modules. The underlying building blocks of the paths are finite tensor products of several perfect crystals. The motivation for this work is an interpretation of fermionic formulas, which arise from the combinatorics of Bethe Ansatz studies of solvable lattice models, as branching functions of affine Lie algebras. It is shown that the conditions for the tensor product theorem are satisfied for coherent families of crystals previously studied by Kang, Kashiwara and Misra, and the coherent family of crystals \Bk,l\l≥ 1 of type An(1).