An Extension of a Result by Steinberg towards a Chevalley Basis Algorithm

Shimura Correspondence for Finite Groups

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).

On Groups with Root System of Type 2 F 4

Let Φ̃ be a root system of type F4, and let G be a group generated by non-trivial subgroups Ar, r ∈ Φ̃, satisfying some generalized Steinberg relations, which are also satisfied by root subgroups corresponding to a Moufang octagon. These relations can be considered as a generalization of the element-wise commutator relations in Chevalley groups. The Steinberg presentation specifies the groups sat...

Block-compatible metaplectic cocycles

has cardinality r ≥ 1. Let G be the F-rational points of a simple Chevalley group defined over F. In his thesis, Matsumoto [5] gave a beautiful construction for the metaplectic cover G̃ of G, a central extension of G by μr(F) whose existence is intimately connected with the deep properties of the r-th order Hilbert symbol (·, ·)F : F × × F → μr(F). Metaplectic groups figure prominently in the st...

On p-semilinear transformations

In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

The Steinberg lattice of a finite Chevalley group and its modular reduction