-vertex Model: Creation Algebras and Quasi-particles I

The infinite configuration space of an integrable vertex model based on Uq gl(2|2) 1 is studied at q = 0. Allowing four particular boundary conditions, the infinite configurations are mapped onto the semi-standard supertableaux of pairs of infinite border strips. By means of this map, a weight-preserving one-to-one correspondence between the infinite configurations and the normal forms of a pair of creation algebras is established for one boundary condition. A pair of type-II vertex operators associated with an infinite-dimensional Uq gl(2|2)-module˚V and its dual˚V * is introduced. Their existence is conjectured relying on a free boson realization. The realization allows to determine the commutation relation satisfied by two vertex operators related to the same Uq gl(2|2)-module. Explicit expressions are provided for the relevant R-matrix elements. The formal q → 0 limit of these commutation relations leads to the defining relations of the creation algebras. Based on these findings it is conjectured that the type II vertex operators associated with˚V and˚V * give rise to part of the eigenstates of the row-to-row transfer matrix of the model. A partial discussion of the R-matrix elements introduced on˚V ⊗ ˚ V * is given.