On the multiplicity spaces of spherical subgroups of minimal rank

Abstract

AbstractLet be a complex connected semisimple Lie group and be a connected semisimple subgroup of . Consider the branching problem of decomposing the simple ‐representations as a sum of simple ‐representations . When , it is the tensor product decomposition. The multiplicity space satisfies , where the sum runs over the isomorphism classes of simple ‐representations. In the case when is spherical of minimal rank, we describe as the intersection of kernels of powers of root operators in some weight space of the dual space of . When , we recover by geometric methods a well‐known result.