On the quantum affine superalgebra Uq(q̂(2|2)) at level one Original Research Article

Motivated by applications to two-dimensional disordered systems this study focuses on evaluation modules Vz, Vz∗ of the quantum current superalgebra Uq(q̂(2|2)) obtained from deformations of infinite-dimensional gl(2||2) representations. A free field realization of Uq(q̂(2|2)) associated to the appropriate non-standard root system is given. The intertwining conditions for vertex operators related to the evaluation modules Vz and Vz∗ are explored to provide bosonized expressions for the coefficients in their formal series expansions. Finally, the existence of one vertex operator is conjectured.