##### Department of Mathematics,

University of California San Diego

****************************

### Algebra Seminar

## Karina Batistelli

## QHWM of the ``orthogonal'' and ``symplectic'' type Lie algebras of the matrix quantum pseudo differential operators

##### Abstract:

n this talk we will characterize the irreducible quasifinite highest weight modules of some subalgebras of the Lie algebra of matrix quantum pseudodifferential operators $N \times N$. In order to do this, we will first give a complete description of the anti-involutions that preserve the principal gradation of the algebra of $N\times N$ matrix quantum pseudodifferential operators and we will describe the Lie subalgebras of its minus fixed points. We will obtain, up to conjugation, two families of anti-involutions that show quite different results when $n=N$ and $n< N$. We will then focus on the study of the ``orthogonal'' and ``symplectic'' type subalgebras found for case $n=N$, specifically the classification and realization of the quasifinite highest weight modules.

Host: Henry Tucker

### January 29, 2018

### 2:00 PM

### AP&M 5829

****************************