Infinitesimal operators and structure of the representations of the groups SO*(2n) and SO(2n) in a U(n) basis and of the groups SU*(2n) and SU(2n) in an Sp(n) basis

Abstract

The infinitesimal operators of the most degenerate representations of the groups SO*(2n) and SU*(2n) are found in a discrete basis. The structure (composition series) of these representations is studied. The classification of unitary irreducible representations of these groups which belong to most degenerate series is given. The infinitesimal operators of irredicuble unitary representations of SO(2n) in a U(n) basis and of SU(2n) in an Sp(n) basis are found for the cases of highest weights (M, M, 0, ..., 0), M≥0.