Invariant functions on symplectic representations
Algebraic Geometry
2010-02-23 v2 Commutative Algebra
Representation Theory
Symplectic Geometry
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.
Cite
@article{arxiv.math/0506171,
title = {Invariant functions on symplectic representations},
author = {Friedrich Knop},
journal= {arXiv preprint arXiv:math/0506171},
year = {2010}
}
Comments
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