We consider the Fourier expansions of automorphic forms on general Lie groups, with a particular emphasis on exceptional groups. After describing some principles underlying known results on GL(n), Sp(4), and G2, we perform an analysis of the expansions on split real forms of E6 and E7 where simplifications take place for automorphic realizations of real representations which have small Gelfand-...

This paper is devoted to the study of the surjective stability of the K -functor for 1 Chevalley groups of type E . This is a particular case of the stability problem for 7 Chevalley groups, which was posed by H. Bass. In this paper, surjective stability of the K -functor is proved under natural conditions on the dimension of the maximal 1 spectrum of a ring and, independently, under a special ...

Jeffrey Adams, University of Maryland. The Chevalley Involution for Real Groups, with applications to the Fubini-Schur Indicator. The Chevalley involution of a complex group is unique up to conjugation, and takes any algebraic representation to its contragredient. The analogue over local fields is subtle. We prove that the Chevalley involution is defined over R, and with an appropriate conditio...

For all almost affine (hyperbolic) Lie superalgebras, the defining relations are computed in terms of their Chevalley generators.

The work of Chevalley ([BIBLE], [Chev61]) and Demazure–Grothendieck [SGA3] provides a satisfactory understanding of the reasons for the existence and uniqueness of “Chevalley groups” over Z. These are the reductive group schemes G → Spec(Z) (i.e., smooth affine groups with connected reductive geometric fibers) for which there exists closed subtorus T ⊂ G over Z that is maximal on geometric fibe...

In finite-dimensional simple Lie algebras and affine Kac-Moody algebras, Chevalley involutions are crucial ingredients of the modular theory. Towards establishing theory for extended we investigate existence “Chevalley involutions” tori algebras. We first discuss how to lift a involution from centerless core which is characterized be torus then entire algebra. prove by type-dependent argument t...

Let G be a simply connected Chevalley group corresponding to an irreducible simply laced root system. Then the finite group G(Z/4Z) has a two fold central extension G(Z/4Z) realized as a Steinberg group. In this paper we construct a natural correspondence between genuine representations of G(Z/4Z) and representations of the Chevalley group G(Z/2Z).