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- W4383473313 abstract "Let $mathfrak g$ be either the Lie superalgebra $mathfrak{gl}(V)oplusmathfrak{gl}(V)$ where $V:=mathbb C^{m|n}$ or the Lie superalgebra $mathfrak{gl}(V)$ where $V:=mathbb C^{m|2n}$. Furthermore, let $W$ be the $mathfrak g$-module defined by $W:=Votimes V^*$ in the former case and $W:=mathcal S^2(V)$ in the latter case. Associated to $(mathfrak g,W)$ there exists a distinguished basis of Capelli operators $left{D^lambdaright}_{lambdainOmega}$, naturally indexed by a set of hook partitions $Omega$, for the subalgebra of $mathfrak g$-invariants in the superalgebra $mathcal{PD}(W)$ of superdifferential operators on $W$. Let $mathfrak b$ be a Borel subalgebra of $mathfrak g$. We compute eigenvalues of the $D^lambda$ on the irreducible $mathfrak g$-submodules of $mathcal{P}(W)$ and obtain them explicitly as the evaluation of the interpolation super Jack polynomials of Sergeev--Veselov at suitable affine functions of the $mathfrak b$-highest weight. While the former case is straightforward, the latter is significantly more complex. This generalizes a result by Sahi, Salmasian and Serganova for these cases, where such formulas were given for a fixed choice of Borel subalgebra." @default.
- W4383473313 created "2023-07-07" @default.
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- W4383473313 date "2023-07-05" @default.
- W4383473313 modified "2023-09-24" @default.
- W4383473313 title "The refined solution to the Capelli eigenvalue problem for $mathfrak{gl}(m|n)oplusmathfrak{gl}(m|n)$ and $mathfrak{gl}(m|2n)$" @default.
- W4383473313 doi "https://doi.org/10.48550/arxiv.2307.02307" @default.
- W4383473313 hasPublicationYear "2023" @default.
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