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## Representations “induced” from factors [closed]

There is a well known concept of induced representation. That is, for groups for example, we take representation of a subgroup and construct representation of the whole group.

Is there way to construct representations of the whole group from reps of its quotient group?

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 Yes; precomposition. This is too elementary a question for MO. – Qiaochu Yuan May 28 2012 at 15:49 I cant find anything searching the word "precomposition". Can u give at least 1 reference where it constructed? – Dan May 28 2012 at 16:34 Take $H \subseteq G$ a normal subgroup, and let $\rho : G/H \to \mathrm{End}(V)$ be a representation. To get a representation of $G$, you compose the quotient map $G \to G/H$ with $\rho$ (i.e. precompose $\rho$ with the quotient map). – MTS May 28 2012 at 16:38 See en.wikipedia.org/wiki/Pullback . – Qiaochu Yuan May 28 2012 at 17:01 Well, what MTS said is really elementary. Actually I interested in constructing reps from quotient reps AND subgroup reps. But i'd better think by myself before asking again =) – Dan May 28 2012 at 17:14