For a real semisimple Lie group, $G$, and a maximal compact subgroup $K$, and an irreducible unitary representation $\pi$ of $G$, let $H_\pi^K$ be the subspace of vectors fixed by $K$. Is the dimension of $H_\pi^K$ always not greater than one?
2026-04-11 12:56:47.1775912207
Is the space of spherical vectors always one (or zero) dimensional?
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