// Workers AI · dad joke modeWhy was rational representation rational? It had a reasonable rep.
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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.
See also
[edit]- Schur functor, used in the classification of irreducible rational representations of the general linear group
References
[edit]- Bialynicki-Birula, A.; Hochschild, G.; Mostow, G. D. (1963). "Extensions of Representations of Algebraic Linear Groups". American Journal of Mathematics. 85 (1). Johns Hopkins University Press: 131–44. doi:10.2307/2373191. ISSN 1080-6377. JSTOR 2373191.
- Springer Online Reference Works: Rational Representation
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