Invariant Differential Operators and an Homomorphism of Harish-Chandra

Invariant Differential Operators and an Homomorphism of Harish-chandra

Invariant Differential Operators and an Homomorphism of Harisb - Chandra

Let 9 be a reductive complex Lie algebra, with adjoint group G, Cartan subalgebra ~ and Weyl group W. Then G acts naturally on the algebra of polynomial functions &'(g) and hence on the ring of differential operators with polynomial coefficients, .97(g). Similarly, W acts on ~ and hence on .97(~). In [BC2], Harish-Chandra defined an algebra homomorphism J : .97(g)G -t .97(~)w. Recently, Wallach...

Invariant Differential Operators and an Homomorphism of Harisb-chandra

Let 9 be a reductive complex Lie algebra, with adjoint group G, Cartan subalgebra ~ and Weyl group W. Then G acts naturally on the algebra of polynomial functions &'(g) and hence on the ring of differential operators with polynomial coefficients, .97(g). Similarly, W acts on ~ and hence on .97(~). In [BC2], Harish-Chandra defined an algebra homomorphism J : .97(g)G -t .97(~)w. Recently, Wallach...

A Capelli Harish-chandra Homomorphism

For a real reductive dual pair the Capelli identities define a homomorphism C from the center of the universal enveloping algebra of the larger group to the center of the universal enveloping algebra of the smaller group. In terms of the Harish-Chandra isomorphism, this map involves a ρ-shift. We view a dual pair as a Lie supergroup and offer a construction of the homomorphism C based solely on...

The Kernel of an Homomorphism of Harish-chandra