A note on the Capelli identities for symmetric pairs of Hermitian type

Details A note on the Capelli identities for symmetric pairs of Hermitian type A note on the Capelli identities for symmetric pairs of Hermitian type

2008-08-05

arxiv.org/abs/0808.0607v1

Mathematics

Representation Theory

29 pages

Scientific paper

We get several identities of differential operators in determinantal form. These identities are non-commutative versions of the formula of Cauchy-Binet or Laplace expansions of determinants, and if we take principal symbols, they are reduced to such classical formulas. These identities are naturally arising from the generators of the rings of invariant differential operators over symmetric spaces, and have strong resemblance to the classical Capelli identities. Thus we call those identities the Capelli identities for symmetric pairs.

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