Invariant functions on symplectic representations
代数几何
2010-02-23 v2 交换代数
表示论
辛几何
摘要
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.
引用
@article{arxiv.math/0506171,
title = {Invariant functions on symplectic representations},
author = {Friedrich Knop},
journal= {arXiv preprint arXiv:math/0506171},
year = {2010}
}
备注
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