In mathematics, the infinitesimal character of an irreducible representation ρ {\displaystyle \rho } of a semisimple Lie group G {\displaystyle G} on a vector space V {\displaystyle 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 {\displaystyle \rho } by two successive linearizations.
In mathematics, the infinitesimal character of an irreducible representation ρ {\displaystyle \rho } of a semisimple Lie group G {\displaystyle G} on a vector space V {\displaystyle 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 {\displaystyle \rho } by two successive linearizations.
Source: Wikipedia "Infinitesimal character" · CC BY-SA 4.0
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