Invariant Differential Operators and an Homomorphism of Harisb - 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 Harish-chandra

0 Symplectic reflection algebras , Calogero - Moser system , and deformed Harish - Chandra homomorphism

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

Symplectic Reflection Algebras, Calogero-moser System, and Deformed Harish-chandra Homomorphism

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

2 4 Ju l 2 00 1 Symplectic reflection algebras , Calogero - Moser space , and deformed

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of P, where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is related to the coordi...