Representation theory of Lie groups

Infinitesimal character

In mathematics, the infinitesimal character of an irreducible representation ρ of a semisimple Lie group G on a vector space V is, roughly speaking, a mapping to scalars that encodes the process of first differentiating and then diagonalizing the representation. It therefore is a way of extracting something essential from the representation ρ by two successive linearizations. (Wikipedia).

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Related pages

Differential operator | Infinitesimal transformation | Schur's lemma | Harish-Chandra isomorphism | Lie algebra | Universal enveloping algebra | Weyl group | Symmetric algebra | Cartan subalgebra | Abuse of notation | Irreducible representation