Finite Crystals and Paths

Details Finite Crystals and Paths Finite Crystals and Paths

1999-01-20

arxiv.org/abs/math/9901082v2

Advanced Studies in Pure Mathematics 28(2000) 113-132

Mathematics

Quantum Algebra

15 pages, LaTeX2e, submitted to the proceedings of the RIMS98 program "Combinatorial Methods in Representation Theory"

Scientific paper

We consider a category of finite crystals of a quantum affine algebra whose objects are not necessarily perfect, and set of paths, semi-infinite tensor product of an object of this category with a certain boundary condition. It is shown that the set of paths is isomorphic to a direct sum of infinitely many, in general, crystals of integrable highest weight modules. We present examples from C_n^{(1)} and A_{n-1}^{(1)}, in which the direct sum becomes a tensor product as suggested from the Bethe Ansatz.

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