The $U_q(\hat{sl}(2/1))_1$-module $V(Λ_2)$ and a Corner Transfer Matrix at q=0

Details The $U_q(\hat{sl}(2/1))_1$-module $V(Λ_2)$ and a Corner Transfer Matrix at q=0 The $U_q(\hat{sl}(2/1))_1$-module $V(Λ_2)$ and a Corner Transfer Matrix at q=0

2003-03-30

arxiv.org/abs/nlin/0303069v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

28 pages, revtex accepted for publication in Nuclear Physics B

Scientific paper

10.1016/S0550-3213(03)00237-2

The north-west corner transfer matrix of an inhomogeneous integrable vertex model constructed from the vector representation of $U_q\bigl(sl(2/1)\bigr)$ and its dual is investigated. In the limit $q\to0$, the spectrum can be obtained. Based on an analysis of the half-infinite tensor products related to all CTM-eigenvalues $\geq -4$, it is argued that the eigenvectors of the corner transfer matrix are in one-to-one correspondance with the weight states of the $U_q\bigl((\hat{sl}(2/1)\bigr)_1-$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 $U_q\bigl(sl(2|1)\bigr)$ to the weight states of $V(\Lambda_2)$ with multiplicity one.

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