Rational representation

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

References

• Bialynicki-Birula, A.; Hochschild, G. Hochschild; 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. (registration required (help)).
• Springer Online Reference Works: Rational Representation