In mathematics, in the

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

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

s, a

linear representation Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essenc ...

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 In mathematics, in particular the subfield of algebraic geometry, a rational map or rational mapping is a kind of partial function between algebraic varieties. This article uses the convention that varieties are irreducible. Definition Formal d ...

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

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