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I studied representation theory of Lie groups and Lie algebras from the book by Brian Hall. I'm now curious about the formulation of the theory for discrete subgroups of Lie groups, mostly matrix Lie groups. Are there any good references on the subject?

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There is a large literature on discrete subgroups of Lie groups. Here are only a few examples.

Discrete subgroups of Lie groups: M. S. Raghunathan

Discrete Subgroups of Lie Groups | Madabusi S

Discrete Subgroups of Semisimple Lie Groups | G. A. Margulis.

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