Related papers: On parahoric subgroups

We prove the even isomorphism theorem for Coxeter groups

In this expository paper we review some recent results about representations of Kac-Moody groups. We sketch the construction of these groups. If practical, we present the ideas behind the proofs of theorems. At the end we pose open…

In this note we study the finite groups whose subgroup lattices are dismantlable.

The main theorem of Galois theory states that there are no finite group-subgroup pairs with the same invariants. On the other hand, if we consider complex linear reductive groups instead of finite groups, the analogous statement is no…

We introduce nil-Hecke algebras for Weyl groupoids. We describe a basis and some properties of these algebras which lead to a notion of Bruhat order for Weyl groupoids.

We give a purely cubical argument for the localization theorem for the cubical version of higher Chow groups.

We give some properties of parabolic inductions and their adjoint functors for pro-$p$-Iwahori Hecke algebras.

We observe that abelian subgroups of Helly groups are finitely generated, and consequently, soluble subgroups of Helly groups are virtually abelian.

We prove that finitely generated relatively hyperbolic groups are bi-exact if and only if all peripheral subgroups are bi-exact. This is a generalization of Ozawa's result which claims that finitely generated relatively hyperbolic groups…

Let G be a split adjoint semisimple group over Q and K a maximal compact subgroup of the real points G(R). We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms on congruence quotients of G(R)/K.…

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We prove the Ptolemaean Inequality and the Theorem of Ptolemaeus in the setting of $H$--type groups of Iwasawa--type.

We overview a web of conjectures about torsors under reductive groups over regular rings and survey some techniques that have been used for making progress on such problems.

We describe the structure of hyperelliptic Rauzy diagrams and hyperelliptic Rauzy-Veech groups. In particular, this provides a solution of the hyperelliptic cases of a conjecture of Zorich on the Zariski closure of Rauzy-Veech groups.

The main results extend to sums over primes in a short interval earlier estimates by the author for "long" Weyl sums over primes.

We give presentations of braid groups and pure braid groups on surfaces.

We study the Whitehead torsions of inertial h-cobordisms, and identify various types representing a nested sequence of subsets of the Whitehead group. A number of examples are given to show that these subsets are all different in general.

We introduce some classical concepts in the representation theory of compact groups, in order to use them for a new generalization of the Peter-Weyl Theorem. We mostly deal with functions on locally compact groups possessing large…

We give a criterion for separability of subgroups of certain outer automorphism groups. This answers questions of Hagen and Sisto, by strengthening and generalizing a result of theirs on mapping class groups.

Reductions of N-wave type equations related to simple Lie algebras and the hierarchy of their Hamiltonian structures are studied. The reduction group G_R is realized as a subgroup of the Weyl group of the corresponding algebra. Some of the…