Date:	Mon, April 30, 2012
Time:	17:15
Place:	Research II Lecture Hall

Abstract: Let $G$ be a complex reductive group and $V$ a representation space of $G$. Then there is a quotient space $Z$ and a canonical map $\pi\colon V\to Z$. The quotient space $Z$ has a natural stratification which reflects properties of the $G$-action on $V$. If $\phi\colon Z\to Z$ is an automorphism, then one can ask the following questions. \begin{enumerate} \item Does $\phi$ automatically preserve the stratification? \item Is there an automorphism $\Phi\colon V\to V$ which lifts $\phi$? In other words, can we have $\pi(\Phi(v))=\phi(\pi(v))$ for all $v\in V$. If so, can we choose $\Phi$ to be equivariant, i.e., so that $\Phi(gv)=g\Phi(v)$ for all $v\in V$ and $g\in G$? \end{enumerate} We give conditions for positive responses to these questions, expanding upon work of Kuttler and Reichstein. Numerous examples will be discussed.