Conjugate representation
= Conjugate representation
{title2=$\bar R$}
For a complex <group representation> with <matrices> $R(g)$, its conjugate representation has <matrices> $\overline{R(g)}$ on the conjugate <vector space>. In a <unitary representation> it is equivalent to the <dual representation>, since $(R(g)^{-1})^T=\overline{R(g)}$. On a diagonal <maximal torus>, its <weights> are the negatives of the original <weights>.