= Alternant character formula for the general linear group
{title2=$\phi_\lambda(x)=A_{\lambda+\delta}(x)/A_\delta(x)$}
For a dominant integer tuple $\lambda$ and $\delta=(m-1,\ldots,0)$, the rational Schur <character> is $\det(x_i^{\lambda_j+m-j})/\det(x_i^{m-j})$. For partitions it is a <symmetric polynomial>; for general tuples it is Laurent on the diagonal torus. The formula follows by comparing the <trace of a permuted tensor power> with the <Frobenius alternant character formula> and using independence of symmetric-group <characters>. Apparent poles at coincident nonzero <eigenvalues> are removable.
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