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• W3104597128 abstract "A depending on a complex parameter $k$ superanalog ${mathcal S}{mathcal L}$ of Calogero operator is constructed; it is related with the root system of the Lie superalgebra ${mathfrak{gl}}(n|m)$. For $m=0$ we obtain the usual Calogero operator; for $m=1$ we obtain, up to a change of indeterminates and parameter $k$ the operator constructed by Veselov, Chalykh and Feigin [2,3]. For $k=1, frac12$ the operator ${mathcal S}{mathcal L}$ is the radial part of the 2nd order Laplace operator for the symmetric superspaces corresponding to pairs $(GL(V)times GL(V), GL(V))$ and $(GL(V), OSp(V))$, respectively. We will show that for the generic $m$ and $n$ the superanalogs of the Jack polynomials constructed by Kerov, Okunkov and Olshanskii [5] are eigenfunctions of ${mathcal S}{mathcal L}$; for $k=1, frac12$ they coinside with the spherical functions corresponding to the above mentioned symmetric superspaces. We also study the inner product induced by Berezin's integral on these superspaces." @default.
• W3104597128 created "2020-11-23" @default.
• W3104597128 creator A5086083415 @default.
• W3104597128 date "2001-01-01" @default.
• W3104597128 modified "2023-09-26" @default.
• W3104597128 title "Superanalogs of the Calogero Operators and Jack Polynomials" @default.
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• W3104597128 doi "https://doi.org/10.2991/jnmp.2001.8.1.7" @default.
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