Capelli elements in the classical universal enveloping algebras (Q2741038)

Let \(\nu\) be a partition of an integer \(n\) into at most \(N\) parts. There is a distinguished basis of the center \(Z(\mathfrak{gl}_N)\) of the universal enveloping algebra \(U(\mathfrak{gl}_N)\) parametrized by these partitions. These are called Capelli elements. An explicit formula for these elements was given earlier by M. Nazarov and A. Okounkov independently. The paper under review finds analogous formulas for Capelli elements in the case of the Lie algebras \(\mathfrak{so}_N\) and \(\mathfrak{sp}_N\).NEWLINENEWLINEFor the entire collection see [Zbl 0963.00024].