Seminar of April 26th

26/04/2018, 14.30 hs, aula 27 FaMAF

Lie subalgebras of the matrix quantum pseudo-differential operators


Speaker: Karina Batistelli

In this talk, we will characterize the irreducible quasi-finite highest weight modules of some subalgebras of the Lie algebra of N×N matrix quantum pseudodifferential operators. 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×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 quasi-finite highest weight modules.