An integrable Uq( gl(2|2))1-model: corner transfer matrices and Young skew diagrams Original Research Article

The path space of an inhomogeneous vertex model constructed from the vector representation of Uq(gl(2|2)) 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 Uq( sl(2|2))/H with grade −n is found for n⩾−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 Uq( sl(2|2)) constructed from an infinite-dimensional Uq(gl(2|2))-module is conjectured.