##### Department of Mathematics,

University of California San Diego

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### Math 295 - Mathematics Colloquium

## Gerry Schwarz

#### Brandeis University

## Representations of invariant differential operators

##### Abstract:

Let $G$ be a group and let $V$ be a finitedimensional $G$-module. Let $B$ denote the algebra of $G$-invariantpolynomial differential operators on $V$. It is natural to pose thefollowing questions:1) What is the representation theory of $B$? What are the primitiveideals of $B$?2) Does $B$ have finite dimensional representations? If so, are theycompletely reducible?medskip oindentLittle is known about these questions when $G$ is noncommutative. Wegive answers for the adjoint representation of SL$_3(C)$, alreadyan interesting and difficult case.

Host: Nolan Wallach

### October 10, 2002

### 4:00 PM

### AP&M 6438

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