= Highest-weight classification of rational GL representations
{title2=$\lambda\in\mathbb Z^m,\quad\lambda_1\ge\cdots\ge\lambda_m$}
The irreducible rational $GL_m$ <modules> are $D_\lambda(V)=(\det V)^{\lambda_m}\otimes D_{\lambda-\lambda_m(1,\ldots,1)}(V)$. The second factor is a <Schur module>. Clearing <determinant> denominators reduces completeness to the <Schur algebra> classification of <polynomial> <modules>. Distinct dominant integer tuples have distinct highest torus weights. Their <characters> are symmetric <Laurent polynomials>; only <polynomial> <modules> have <characters> defined at every singular endomorphism.
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