Generalizing the MVW involution, and the contragredient
Generalizing the MVW involution, and the contragredient
For certain quasi-split reductive groups $G$ over a general field $F$, we construct an automorphism $\iota_G$ of $G$ over $F$, well-defined as an element of ${\rm Aut}(G)(F)/jG(F)$ where $j:G(F) \rightarrow {\rm Aut}(G)(F)$ is the inner-conjugation action of $G(F)$ on $G$. The automorphism $\iota_G$ generalizes (although only for quasi-split groups) an …