## Divisibility theorems for group representations IIOctober 14, 2009

Posted by Akhil Mathew in algebra, representation theory.
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Given a group ${G}$ and a subgroup ${H}$ (in fact, this can be generalized to a non-monomorphic map ${H \rightarrow G}$), a representation of ${G}$ yields by restriction a representation of ${H}$. One obtains a functor ${\mathrm{Res}^G_H: Rep(G) \rightarrow Rep(H)}$. This functor has an adjoint, denoted by ${\mathrm{Ind}_H^G: Rep(H) \rightarrow Rep(G)}$. (more…)