##### Department of Mathematics,

University of California San Diego

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### University of California Lie Theory Workshop

## Vera Serganova

#### University of California, Berkeley

## \bf \huge On the category of bounded $(g,k)$-modules

##### Abstract:

This talk is based on my joint work with I. Penkov. Let g be a simple Lie algebra, and $k$ be a reductive subalgebra in $g. A (g,k)-$module $M$ is bounded if it is locally finite over $k$ and the multiplicities of all irreducible finite-dimensional modules in $M$ are uniformly bounded. (Two examples from classical representation theory are ladder modules in Harish-Chandra theory and cuspidal modules in case when $k$ is a Cartan subalgebra). I will formulate several general results about bounded modules involving primitive ideals theory and geometry (localization). Then I concentrate on the example when $g=B_2$, and $k$ is the principal $sl(2)-$subalgebra, where the complete classification of irreducible simple bounded $(g,k)-$modules is done.

Host: Efim Zelmanov

### February 16, 2008

### 10:10 AM

### NSB 1205

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