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

R. M. Gade

doi:10.1016/S0550-3213(03)00237-2

paper

The $U_{q} (s l^(2/1))_{1}$ -module $V (Λ_{2})$ and a Corner Transfer Matrix at q=0

arXiv:nlin/0303069 · doi:10.1016/S0550-3213(03)00237-2

Abstract

The north-west corner transfer matrix of an inhomogeneous integrable vertex model constructed from the vector representation of $U_{q} (s l (2/1))$ 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 $\geq - 4$ , it is argued that the eigenvectors of the corner transfer matrix are in one-to-one correspondance with the weight states of the $U_{q} ((s l^(2/1))_{1} -$ module $V (Λ_{2})$ 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 $U_{q} (s l (2∣1))$ to the weight states of $V (Λ_{2})$ with multiplicity one.

28 pages, revtex accepted for publication in Nuclear Physics B

The Uq​(sl^(2/1))1​-module V(Λ2​) and a Corner Transfer Matrix at q=0

Abstract

The $U_{q} (s l^(2/1))_{1}$ -module $V (Λ_{2})$ and a Corner Transfer Matrix at q=0