1998/11/22 by Maxim Nazarov
Mathematics · #math.RT #math.CO #math.QA
published as Adv. Studies Pure Math. 28 (2000), 261-285 · 24 pages, AmS-TeX
arxiv created 1998/11/22 · arxiv updated 2009/11/30
For any complex classical group G=ON,SpN consider the ring Z(g) of G-invariants in the corresponding enveloping algebra U(g). Let u be a complex parameter. For each n=0,1,2,... and every partition ν of n into at most N parts we define a certain rational function Zν(u) which takes values in Z(g). Our definition is motivated by the works of Cherednik and Sklyanin on the reflection equation, and also by the classical Capelli identity. The degrees in U(g) of the values of Zν(u) do not exceed n. We describe the images of these values in the n-th symmetric power of g. Our description involves the plethysm coefficients as studied by Littlewood, see Theorem 3.4 and Corollary 3.6.