##### Department of Mathematics,

University of California San Diego

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### Representation Theory Seminar

## Amit Trehan

## Lifting of characters over metaplectic covers of ${\tensy SL(n)}$ over a ${\tensy p}$-adic field

##### Abstract:

We generalize the approach of Adams by obtaining a character fornula relating the irreducible characters of $PGL(n)$ with those of certain covers of $SL(n)$. We then study the lifting of functions between covers of $SL(n)$ and $PGL(n)$. We use orbital integrals to obtain a formula for the lifting of characters as a dual to the formula relating the characters. This is based on the approach of Kazhdan and Flicker.

### November 21, 2006

### 2:00 PM

### AP&M 7218

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