For Sp(p,q), the spin norm strictly increases along any Vogan pencil once it goes beyond the unitarily small convex hull.
Vogan, Singular unitary representations , Noncommutative harmonic analysis and Lie groups (Mar- seille, 1980), 506–535
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Distribution of spin norm along pencils: the $Sp(p, q)$ case
For Sp(p,q), the spin norm strictly increases along any Vogan pencil once it goes beyond the unitarily small convex hull.