Invariant functions on symplectic representations

Abstract

Let G be a connected reductive group. In this paper we are studying the invariant theory of symplectic G-modules. Our main result is that the invariant moment map is equidimensional. We deduce that the categorical quotient is a fibration over an affine space with rational generic fibers. Of particular interest are those modules for which the generic orbit is coisotropic. We prove that they are cofree. This result has been used in another paper (math.SG/0505268) to classify all these modules. Our main tool is a symplectic version of the local structure theorem.

v1: 24 pages; v2: 31 pages, expanded exposition, new introduction, some facts (esp. Thm. 7.2+Corollaries, Thm. 8.4) which were only implicit in v1 are now spelled out

References in corpus (1)

• Classification of multiplicity free symplectic representations

Cited by in corpus (7)

• Classification of multiplicity free symplectic representations
• Computation of Weyl groups of G-varieties
• On fibers of algebraic invariant moment maps
• Polar symplectic representations
• Algebraic Hamiltonian actions
• Cohomological integrality for weakly symmetric representations of reductive groups
• Lifting central invariants of quantized Hamiltonian actions