Finite-Dimensional Crystals B^{2,s} for Quantum Affine Algebras of type D_{n}^{(1)}

Abstract

The Kirillov--Reshetikhin modules W^{r,s} are finite-dimensional representations of quantum affine algebras U'_q(g), labeled by a Dynkin node r of the affine Kac--Moody algebra g and a positive integer s. In this paper we study the combinatorial structure of the crystal basis B^{2,s} corresponding to W^{2,s} for the algebra of type D_n^{(1)}.

34 pages; final version to appear in J. Alg. Combin

References in corpus (3)

• X=M for symmetric powers
• Virtual crystals and Kleber's algorithm
• t-analogue of the q-characters of finite dimensional representations of quantum affine algebras

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• Combinatorial structure of Kirillov-Reshetikhin crystals of type D_n(1), B_n(1), A_{2n-1}(2)
• Soliton cellular automaton associated with $G_2^{(1)}$ crystal base
• Uniform description of the rigged configuration bijection
• Soliton cellular automaton associated with $D_n^{(1)}$-crystal $B^{2,s}$
• Applications of Crystal Bases to Current Problems in Representation Theory