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arXiv · 1712.06266

Super Jack-Laurent Polynomials

A. N. Sergeev
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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 $k[\varepsilon]^{\otimes r}$.

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A. N. Sergeev. 2017-12-18. Super Jack-Laurent Polynomials. https://arxiv.org/abs/1712.06266

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