QHWM of the ``orthogonal'' and ``symplectic'' types Lie subalgebras of the matrix quantum pseudodifferential operators.

CARINA BOYALLIAN; KARINA BATISTELLI

San Diego

Congreso; Joint Mathematical Meeting 2018; 2018

In this talk we will characterize the irreducible quasifinite highest weight modules of some subalgebras of the Lie algebra of matrix quantum pseudodifferential operators N x 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 $N imes N$ 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