论文标题
Capelli操作员特征值的明确公式Superalgebra $ \ frak {osp}（1 | 2n）$
Explicit formulas for Eigenvalues of Capelli operators for the Lie superalgebra $\frak{osp}(1|2n)$
论文作者
论文摘要
我们定义了$ \ frak {gosp}（1 | 2n）$的代数的自然基础 - 仿射超空间$ \ mathbb {c}^{1 | 2n} $上的不变差分运算符。我们证明，这些操作员位于$ \ frak {gosp}（1 | 2n）$的包裹代数的中心的图像中。使用此结果，我们在$ \ Mathcal {p}（\ Mathbb {C}^{1 | 2n}）$上，计算这些运营商的特征值的显式公式。这解决了在萨希 - 萨尔马马 - 塞尔加诺瓦州未解决的案例中，正骨的capelli特征值问题。我们的主要技术依赖于具有多项式条目的某个决定因素的明确计算。
We define a natural basis for the algebra of $\frak{gosp}(1|2n)$-invariant differential operators on the affine superspace $\mathbb{C}^{1|2n}$. We prove that these operators lie in the image of the centre of the enveloping algebra of $\frak{gosp}(1|2n)$. Using this result, we compute explicit formulas for the eigenvalues of these operators on irreducible summands of $\mathcal{P}(\mathbb{C}^{1|2n})$. This settles the Capelli eigenvalue problem for orthosymplectic Lie superalgebras in the cases that were not addressed in Sahi-Salmasian-Serganova. Our main technique relies on an explicit calculation of a certain determinant with polynomial entries.
