Eisenstein Series Arising from Jordan Algebras

We describe poles and the corresponding residual automorphic representations of Eisenstein series attached to maximal parabolic subgroups whose unipotent radicals admit Jordan algebra structure.

UNITRIANGULAR FACTORIZATION OF TWISTED CHEVALLEY GROUPS

Unitriangular factorization is a presentation of a linear group as a product of unipotent radicals of a Borel subgroup and its opposite. Whether this decomposition is known for Chevalley groups over rings of stable rank 1 and some Dedekind rings of arithmetic type, the case of twisted groups has been studied only over finite fields. In the present paper we give a much simpler proof for twisted groups over finite fields and the field of complex numbers.