Rational representation of an algebraic group
= Rational representation of an algebraic group
{title2=$\rho:G\to GL(W)$}
{wiki=Rational_representation}
= Rational representation
{synonym}
A <rational representation> is a <group homomorphism> whose matrix coefficients are <regular functions> on the <affine algebraic group>. For the <general linear group>, those functions are <polynomials> in matrix entries and the inverse <determinant>. The word rational does not permit poles at points of the group.