Generic transfer for general spin groups

Abstract

We prove Langlands functoriality for the generic spectrum of general spin groups (both odd and even). Contrary to other recent instances of functoriality, our resulting automorphic representations on the general linear group are not self-dual. Together with cases of classical groups, this completes the list of cases of split reductive groups whose $L$-groups have classical derived groups. The important transfer from ${\mathrm{GSp}}_4$ to ${\mathrm{GL}}_4$ follows from our result as a special case