Mathematics – Quantum Algebra
Scientific paper
2001-11-27
Journal of Algebra 267 (2003) 212-245
Mathematics
Quantum Algebra
27 pages; error corrected
Scientific paper
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 $\{B^{k,l}\}_{l\ge 1}$ of type $A_n^{(1)}$.
Okado Masato
Schilling Anne
Shimozono Mark
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