Branching laws for spherical harmonics on superspaces in exceptional cases

Abstract

Abstract It turns out that harmonic analysis on the superspace Rm|2n is quite parallel to the classical theory on the Euclidean space Rm unless the superdimension M:=m-2n is even and non-positive. The underlying symmetry is given by the orthosymplectic superalgebra osp(m|2n). In this paper, when the symmetry is reduced to osp(m-1|2n) we describe explicitly the corresponding branching laws for spherical harmonics on Rm|2n also in exceptional cases, i.e, when M − 1 ∈ −2N0. In unexceptional cases, these branching laws are well-known and quite analogous as in the Euclidean framework.