On the Decomposition of a Representation of SOn When Restricted to SOn-1

Abstract

Let k be a local field, with char(k) ≠ 2. A quadratic space V over k is a finite dimensional vector space together with a non-degenerate quadratic form Q: V → k.The special orthogonal group SO(V) consists of all linear maps T: V → V which satisfy:Q(Tv) = Q(v) for all ν and det T = 1.