Determinant twist
= Determinant twist
{title2=$g\longmapsto(\det g)^r\rho(g)$}
Tensoring a <rational representation> of the <general linear group> with a <determinant> power shifts every highest-weight coordinate by the same integer $r$. Positive twists can clear <determinant> denominators; negative twists supply <rational representations> that do not extend to singular matrices. Twisting preserves irreducibility and dimension.