Distribution of spin norm along pencils: the $Sp(p, q)$ case

TL;DR

This paper investigates how the spin norm behaves along Vogan pencils in the context of the symplectic group $Sp(p, q)$, demonstrating a strict increase beyond a certain convex hull.

Contribution

It extends previous work by proving the strict increase of the spin norm along Vogan pencils for $Sp(p, q)$ beyond the unitarily small convex hull.

Findings

Spin norm strictly increases along Vogan pencils beyond the convex hull.

Extends previous results to the case of $Sp(p, q)$.

Provides new insights into the structure of $Sp(p, q)$ representations.

Abstract

As a sequel to [2] and Theorem C of [3], this paper shows that for $Sp(p,q)$, the spin norm strictly increases along any Vogan pencil once it goes beyond the unitarily small convex hull.