= Rational representation of the general linear group
{title2=$\rho_{ij}\in\mathbb C[g_{ab},\det(g)^{-1}]$}
= Rational GL representation
{synonym}
The matrix coefficients of a rational $GL_m$ action belong to its <coordinate ring> $\mathbb C[g_{ab},\det(g)^{-1}]$. Multiplying the action by a sufficiently large <determinant twist> clears all <determinant> denominators and produces a <polynomial representation>. Irreducible rational actions are indexed by decreasing integer highest weights, with negative coordinates allowed.
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