The $U_q(\widehat{sl}(2/1){)}_1$-module $V({\Lambda }_2)$ and a Corner Transfer Matrix at q=0

Abstract

The north-west corner transfer matrix of an inhomogeneous integrable vertex model constructed from the vector representation of $U_q(sl(2/1))$ and its dual is investigated. In the limit $q\to 0$, the spectrum can be obtained. Based on an analysis of the half-infinite tensor products related to all CTM-eigenvalues $\ge -4$, it is argued that the eigenvectors of the corner transfer matrix are in one-to-one correspondance with the weight states of the $U_q((\widehat{sl}(2/1){)}_1-$module $V({\Lambda }_2)$ at level one. This is supported by a comparison of the comlete set of eigenvectors with a nondegenerate triple of eigenvalues of the CTM-Hamiltonian and the generators of the Cartan-subalgebra of $U_q(sl(2|1))$ to the weight states of $V({\Lambda }_2)$ with multiplicity one.

28 pages, revtex accepted for publication in Nuclear Physics B

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• Algebraic Bethe ansatz for an integrable U_q[Sl(n|m)] vertex model with mixed representations
• An integrable $U_q(\widehat{gl}(2|2){)}_1$-Model: Corner Transfer Matrices and Young Skew Diagrams