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

|title = Extensions of Representations of Algebraic Linear Groups

|last1 = Bialynicki-Birula

|first1 = A.

|last2 = Hochschild

|first2 = G.

|last3 = Mostow

|first3 = G. D.

|issn = 1080-6377

|volume = 85

|issue = 1

|year = 1963

|pages = 131–44

|doi = 10.2307/2373191

|jstor = 2373191

}}

[https://www.encyclopediaofmath.org/index.php/Rational_representation Springer Online Reference Works: Rational Representation]