Rational representation

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In mathematics, in the representation theory of algebraic groups, a linear representation of an algebraic group is said to be rational if, viewed as a map from the group to the general linear group, it is a rational map of algebraic varieties.

Finite direct sums and products of rational representations are rational.

A rational module is a module that can be expressed as a sum (not necessarily direct) of rational representations.


  • Bialynicki-Birula, A.; Hochschild, G.; Mostow, G. D. (1963). "Extensions of Representations of Algebraic Linear Groups". American Journal of Mathematics. Johns Hopkins University Press. 85 (1): 131–44. doi:10.2307/2373191. ISSN 1080-6377. JSTOR 2373191 – via JSTOR.
  • Springer Online Reference Works: Rational Representation