A Uq(glˆ(2|2))1-vertex model: Creation algebras and quasi-particles I

The infinite configuration space of an integrable vertex model based on Uq(glˆ(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 realisation. The realisation 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.