Algebraic contragredient representation
= Algebraic contragredient representation
{title2=$(\pi^*(g)\ell)(v)=\ell(\pi(g^{-1})v)$}
The algebraic contragredient acts on the entire algebraic <dual space>. It need not be a <smooth representation>, even if the original representation is smooth. Taking the inverse in this formula is necessary to obtain a group action, and inverts a one-dimensional <linear character>.