Dual of a rational Schur module
= Dual of a rational Schur module
{title2=$D_\lambda^*\cong D_{(-\lambda_m,\ldots,-\lambda_1)}$}
The dual of $D_\lambda$ has dominant label $-w_0\lambda=(-\lambda_m,\ldots,-\lambda_1)$. Substitution $x_i\mapsto x_i^{-1}$ in the <alternant character formula for the general linear group> and reversal of determinant columns gives that <character>. The numerator and denominator reversal signs and common <monomial> factors cancel.