  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.
