Capelli Identities for Classical Lie Algebras

Abstract

We extend the Capelli identities (1890) from the Lie algebra $g{l}_N$ to the other two classical Lie algebras $s{o}_N$ and $s{p}_N$. We employ the theory of reductive dual pairs due to Howe. Our technique comes from the representation theory of Yangians.

34 pages, AmS-TeX, the final version