Classification of multiplicity free symplectic representations
نویسنده
چکیده
Let G be a connected reductive group acting on a finite dimensional vector space V . Assume that V is equipped with a G-invariant symplectic form. Then the ring O(V ) of polynomial functions becomes a Poisson algebra. The ring O(V ) of invariants is a sub-Poisson algebra. We call V multiplicity free if O(V ) is Poisson commutative, i.e., if {f, g} = 0 for all invariants f and g. Alternatively, G also acts on the Weyl algebra W(V ) and V is multiplicity free if and only if the subalgebra W(V ) of invariants is commutative. In this paper we classify all multiplicity free symplectic representations.
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