Quommutator deformations of spl(N,1)

Abstract

We analyse the Witten-Woronowicz's type deformations of the Lie superalgebras spl(N,1) and obtain deformations parametrized by N(N-1)/2 independent parameters for N>2 and by three parameters for N=2. For some of these algebras, finite dimensional representations can be constructed in terms of finite difference operators, providing operators that are relevant for the classification of quasi exactly solvable, finite difference equations.