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单词 Representation
释义

Representation

The representation of a Group on a Complex Vector Space is a group action of on by linear transformations. Two finite dimensional representations on and on are equivalentif there is an invertible linear map such that for all . is said to beirreducible if it has no proper Nonzero invariant Subspaces.

See also Character (Multiplicative), Peter-Weyl Theorem, Primary Representation, Schur's Lemma


References

Knapp, A. W. ``Group Representations and Harmonic Analysis, Part II.'' Not. Amer. Math. Soc. 43, 537-549, 1996.


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