Group representation theory MOC

Equivalence of representations

Two group representations of carried by and respectively are equivalent, written , iff the following interchangeable conditions hold rep2

• there exists a Natural isomorphism between ;
• there exists a -linear isomorphism or intertwiner such that for all ;
• and are isomorphic as [[Module over a group|-modules]], written .

Properties

• If is unitary then it is a Unitary equivalence of representations
• Every finite complex representation of a compact group is equivalent to a unitary representation

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