nLab
restricted representation

Context

Representation theory

Ingredients

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Definitions

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Geometric representation theory

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Theorems

Contents

Idea

Given a group GG and a representation VV of GG, then any subgroup inclusion HGH\hookrightarrow G makes also HH act on VV, this is the restricted representation.

Given an irreducible representation of GG, then its decomposition as a direct sum of irreducible representations of HH, after restricting the respesentation to HH, is often called the “branching rule” of the restriction.

More generally, for any group homomorphism HGH \to G representations of GG “pull back” to representations of GG.

The left adjoint to this construction is the operation of forming induced representations, the right adjoint that of coinduced representations.

Examples

References

Last revised on March 5, 2017 at 04:51:01. See the history of this page for a list of all contributions to it.