Matrix Computations of CorwinGreenleaf Multiplicity Functions for Special Unitary Group G = SU (m,n))

Abstract

In this paper, CorwinGreenleaf multiplicity functions for special unitary group have been studied in the light of the Kirillov–Kostant Theory. This was pioneered by the famous mathematician L. Corwin and F.Greenleaf. The multiplicity function is defined as n(Ο^G_π,O^H_ν)=#((O^G_π∩pr^-1(O^G_π))/H).In the case where G = SU(m,n), it has been shown that n(O^G_π,O^H_ν)is at most one.