mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

, in the

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

algebraic group In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory. Man ...

s, 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

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

References

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Springer Online Reference Works: Rational Representation
Representation theory of algebraic groups {{algebra-stub