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## Super Jack-Laurent Polynomials

Algebras and Representation Theory. 2018. Vol. 21. No. 5. P. 1177-1202.

Let Dn,m be the algebra of quantum integrals of the deformed Calogero-Moser-Sutherland problem corresponding to the root system of the Lie superalgebra gl(n, m). The algebra Dn,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 multiplicity free and we prove that the image of the algebra Dn,m in the algebra of endomorphisms of the generalised eigenspace is k[ε]⊗r where k[ε] is the algebra of dual numbers. The corresponding representation is the regular representation of the algebra k[ε]⊗r .