An integrable $U_q(\hat{gl}(2|2))_1$-Model: Corner Transfer Matrices and Young Skew Diagrams

Abstract

The path space of an inhomogeneous vertex model constructed from the vector representation of $U_q\bigl(gl(2|2)\bigr)$ and its dual is studied for various choices of composite vertices and assignments of $gl(2|2)$-weights. At $q=0$, the corner transfer matrix Hamiltonian acts trigonally on the space of half-infinite configurations subject to a particular boundary condition. A weight-preserving one-to-one correspondence between the half-infinite configurations and the weight states of a level-one module of $U_q\bigl(\hat{sl}(2|2)\bigr)/{\cal H}$ with grade $-n$ is found for $n\geq-3$ if the grade $-n$ is identified with the diagonal element of the CTM Hamiltonian. In each case, the module can be decomposed into two irreducible level-one modules, one of them including infinitely many weight states at fixed grade. Based on a mapping of the path space onto pairs of border stripes, the character of the reducible module is decomposed in terms of skew Schur functions. Relying on an explicit verification for simple border stripes, a correspondence between the paths and level-zero modules of $U_q\bigl(\hat{sl}(2|2)\bigr)$ constructed from an infinite-dimensional $U_q\bigl(gl(2|2)\bigr)$-module is conjectured.