This is the second in a series of papers developing a theory of total positivity for loop groups. In this paper, we study infinite products of Chevalley generators. We show that the combinatorics of infinite reduced words underlies the theory, and develop the formalism of infinite sequences of braid moves, called a braid limit. We relate this to a partial order, called the limit weak order, on ...

We prove that the $\mathbb{F}_p[[t]]$-standard Hausdorff spectrum of a compact $\mathbb{F}_p[[t]]$-analytic group contains real interval and it coincides with full unit when is soluble. Moreover, we show classical Chevalley groups over $\mathbb{F}_p[[t]]$ not full, since 1 an isolated point thereof.

Inspired by the work of Chevalley and Eilenberg on de Rham cohomology compact Lie groups, we prove that, under certain algebraic topological conditions, associated to left-invariant elliptic, even hypocomplex, involutive structures groups can be computed using only algebras, thus reducing analytical problem a purely one. The main tool is Leray spectral sequence that connects result obtained Bot...

We use the Steenrod algebra to study the Chow ring CH∗BG of the classifying space of an algebraic group G. We describe a localization property which relates a given G to its elementary abelian subgroups, and we study a number of particular cases, namely symmetric groups and Chevalley groups. It turns out that the Chow rings of these groups are completely determined by the abelian subgroups and ...

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...