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...

For a split semisimple Chevalley group scheme G with Lie algebra g over an arbitrary base scheme S, we consider the quotient of g by the adjoint action of G. We study in detail the structure of g over S. Given a maximal torus T with Lie algebra t and associated Weyl group W , we show that the Chevalley morphism π : t/W → g/G is an isomorphism except for the group Sp2n over a base with 2-torsion...

The purpose of this work is to initiate a combinatorial study of the Bruhat-Chevalley ordering on certain sets of permutations obtained by omitting the parentheses from their standard cyclic notation. In particular, we show that these sets form bounded, graded, unimodal, rank-symmetric and EL-shellable posets. Moreover, we determine the homotopy types of the associated order complexes. Résumé. ...

We continue the study, begun in [11], of inverse Chevalley formulas for equivariant K-group semi-infinite flag manifolds. Using language alcove paths, we reformulate and extend our combinatorial formula to arbitrary weights all simply-laced types (conjecturally also type E8).

We prove a new uniform bound for subgroup growth of a Chevalley group G over the local ring F[[t]] and also over local pro-p rings of higher Krull dimension. This is applied to the determination of congruence subgroup growth of arithmetic groups over global fields of positive characteristic. In particular, we show that the subgroup growth of SLn(Fp[t]) (n ≥ 3) is of type nlog n . This was one o...