A Capelli Harish-Chandra homomorphism

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...

Verma modules , Harish - Chandra ’ s homomorphism

The Harish-Chandra homomorphism is due to [Harish-Chandra 1951]. Attention to universal modules with highest weights is in ]Harish-Chandra 1951], [Cartier 1955], as well as [Verma 1968], [BernsteinGelfand-Gelfand 1971a], [Bernstein-Gelfand-Gelfand 1971b], [Bernstein-Gelfand-Gelfand 1975]. See also [Jantzen 1979]. [1℄ We treat sl(2) in as simple a style as possible, to highlight ideas. Then sl(3...

A Harish-Chandra Homomorphism for Reductive Group Actions

Consider a semisimple complex Lie algebra g and its universal enveloping algebra U(g). In order to study unitary representations of semisimple Lie groups, Harish-Chandra ([HC1] Part III) established an isomorphism between the center Z(g) of U(g) and the algebra of invariant polynomials C[t] . Here, t ⊆ g is a Cartan subspace and W is the Weyl group of g. This is one of the most basic results in...

The Kernel of an Homomorphism of Harish-chandra

Deformed Harish-chandra Homomorphism for the Cyclic Quiver

In the case of cyclic quiver we prove that the deformed Harish-Chandra map whose existence was conjectured by Etingof and Ginzburg is well defined. As an application we prove Kirillov-type formula for the cyclotomic Bessel function.