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Questions about the branch of algebra that deals with groups.

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Does a group representation being transitive on a basis imply irreducibility?

Let $G$ be an infinite discrete group and $\pi$ a representation of $G$ on the Hilbert space $H$. Suppose that the group representation is transitive on an orthonormal basis $B = \{e_j\}_{j=1}^{\infty …
Filipe Viseu's user avatar