Capelli Identities for Classical Lie Algebras

Details Capelli Identities for Classical Lie Algebras Capelli Identities for Classical Lie Algebras

1997-12-07

arxiv.org/abs/q-alg/9712021v3

Math. Ann. 313 (1999), 315-357

Mathematics

Quantum Algebra

34 pages, AmS-TeX, the final version

Scientific paper

We extend the Capelli identities (1890) from the Lie algebra $gl_N$ to the
other two classical Lie algebras $so_N$ and $sp_N$. We employ the theory of
reductive dual pairs due to Howe. Our technique comes from the representation
theory of Yangians.

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