Twisted composition algebras and Arthur packets for triality $\operatorname{Spin}_8$

The purpose of this paper is to construct and analyze certain square-integrable automorphic forms on the quasi-split simply-connected groups $\operatorname{Spin}_8$ of type $D_4$ over a number field $F$. Since the outer automorphism group of $\operatorname{Spin}_8$ is $S_3$, these quasi-split groups are parametrised by étale cubic $F$-algebras $E$ and we denote them by $\operatorname{Spin}^E_8$ (to indicate the dependence on $E$). We shall specialize to the case when $E$ is a cubic field: this gives the so-called triality $\operatorname{Spin}_8$.

Full Text (PDF format)

W.T.G. is partially supported by a Singapore government MOE Tier 1 grant R-146-000-320-114.

G. Savin is partially supported by a National Science Foundation grant DMS-1901745.

Received 14 June 2021

Received revised 29 December 2021

Accepted 10 January 2022

Published 12 January 2023