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On the Decomposition of a Representation of SO<sub>n</sub> When Restricted to SO<sub>n-1</sub>
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 …