Title: Super Jack-Laurent Polynomials,
Abstract: Let $\mathcal{D}_{n,m}$ be the algebra of the quantum integrals of the
deformed Calogero-Moser-Sutherland problem corresponding to the root system of
the Lie superalgebra $\frak{gl}(n,m)$. The algebra $\mathcal{D}_{n,m}$ acts
naturally on the quasi-invariant Laurent polynomials and we investigate the
corresponding spectral decomposition. Even for general value of the parameter
$k$ the spectral decomposition is not simple and we prove that the image of the
algebra $\mathcal{D}_{n,m}$ in the algebra of endomorphisms of the generalised
eigen-space is $k[\varepsilon]^{\otimes r}$ where $k[\varepsilon]$ is the
algebra of the dual numbers the corresponding representation is the regular
representation of the algebra $k[\varepsilon]^{\otimes r}$.