On the SO(n + 3) to SO(n) branching multiplicity space

Abstract

We study the decomposition as an SO(3)-module of the multiplicity space corresponding to the branching from SO(n + 3) to SO(n). Here, SO(n) (resp. SO (3)) is considered embedded in SO(n + 3) in the upper left-hand block (resp. lower right-hand block). We show that when the highest weight of the irreducible representation of SO(n) interlaces the highest weight of the irreducible representation of SO(n + 3), then the multiplicity space decomposes as a tensor product of ⌊(n + 2)/2⌋ reducible representations of SO(3).