Perfect Crystals for U_q(D_4^{(3)})

Details Perfect Crystals for U_q(D_4^{(3)}) Perfect Crystals for U_q(D_4^{(3)})

2006-10-28

arxiv.org/abs/math/0610873v1

J.Algebra317:392-423,2007

Mathematics

Quantum Algebra

27 pages

Scientific paper

10.1016/j.jalgebra.2007.02.021

A perfect crystal of any level is constructed for the Kirillov-Reshetikhin
module of $U_q(D_4^{(3)})$ corresponding to the middle vertex of the Dynkin
diagram. The actions of Kashiwara operators are given explicitly. It is also
shown that this family of perfect crystals is coherent. A uniqueness problem
solved in this paper can be applied to other quantum affine algebras.

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