QHWM of the symplectic and orthogonal type Lie subalgebras of the matrix quantum pseudo-differential operators

CARINA BOYALLIAN; KARINA BATISTELLI

Eugene

Seminario; Algebra seminar; 2018

In this talk we will characterize the irreducible quasifinite highest weight modules ofsome subalgebras of the Lie algebra of matrix quantum pseudodifferential operators N xN.In order to do this, we will first give a complete description of the anti-involutions thatpreserve the principal gradation of the algebra of N ×N matrix quantum pseudodifferentialoperators 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 whenn = 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 thequasifinite highest weight modules.