Primary Representation

Let $\pi$ be a unitary Representation of a Group $G$ on a separable Hilbert Space, and let $R(\pi)$ be the smallest weakly closed algebra of bounded linear operators containing all $\pi(g)$ for $g\in G$. Then $\pi$ is primary if the center of $R(\pi)$ consists of only scalar operations.

References

Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.