Let $G$ be a locally compact group, $\rho$ an irreducible unitary representation on some inner product space $V$. Is there a bound on the dimension of $V$ with respect to the cardinality of the group? If $G$ is finite, then $dim(V) \leq |G|$, is this inequality generalizable? What if we restrict to Hilbert spaces?
2026-03-25 09:48:50.1774432130
Dimension of vector space for irreducible representations
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