MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I am looking for a reference for basic facts about actions of linear algebraic groups and their Lie-algebras on $\mathcal O_X$-modules.

For example I could not find a reference the following:

Let $G$ be a connected, complex linear algebraic group. Then an $\mathcal O_X$-linear map between two $G$-equivariant $\mathcal O_X$-modules commutes with the group actions iff it commutes with the Lie-algebra actions.

share|cite|improve this question
Chapter 5, section 1 of Chriss and Ginzburg contains many nice facts about $G$-equivariant $\mathcal{O}$-modules. However, they do not discuss Lie algebra actions at all. – Mike Skirvin Nov 18 '10 at 15:52

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.