We prove a higher-dimensional Chevalley restriction theorem for orthogonal groups, which was conjectured by Chen and Ngô reductive groups. In characteristic p>2, we also weaker statement. 0, the implies that categorical quotient of commuting scheme diagonal adjoint action group is integral normal. As applications, deduce some trace identities certain multiplicative property Pfaffian over an arb...

A new geometric proof is given for the standard description of subgroups in the Chevalley group G = G(F4, R) of type F4 over a commutative ring R that are normalized by the elementary subgroup E(F4, R). There are two major approaches to the proof of such results. Localization proofs (Quillen, Suslin, Bak) are based on a reduction in the dimension. The first proofs of this type for exceptional g...

Let $$\mathfrak {m}$$ be the Monster Lie algebra. We summarize several interrelated constructions of group analogs for . Our are Chevalley and Kac–Moody groups their generators relations.

This thesis is concerned with the structure theory of generalized Levi subgroups G of simply-connected Chevalley groups defined over a finite extension of a p-adic field. We present a geometric parameterization of this structure known as the Bruhat-Tits building B(G). The building facilitates visualizing and reasoning about the structure ofG, and therefore has applications to all things related...