Related papers: On parahoric subgroups
We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.
We prove that the category of generalized holomorphically contractible families possesses maximal and minimal objects. Moreover, we present basic properties of these extremal families.
Let W be a Weyl group. We can define the notion of positivity of a W-module in terms of the corresponding module over the asymptotic Iwahori-Hecke algebra. We state a conjecture which says that certain explicit W-modules are positive and we…
We prove that a non-elementary relatively hyperbolic group is statistically hyperbolic with respect to every finite generating set. We also establish statistical hyperbolicity for certain direct products of two groups, one of which is…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite dimensional CAT(0)-space.
In a series of recent papers we extended the notion of square integrability, for representations of nilpotent Lie groups, to that of stepwise square integrability. There we discussed a number of applications based on the fact that…
Parahoric group schemes are certain possibly non-reductive, smooth, affine integral models of reductive group schemes defined over a henselian discretely valued field $K$ whose residue field is perfect. We show that any such group scheme…
In this paper, we define and study a kind of Steinberg representation for linear algebraic groups of a particular kind, called groups of parahoric type, defined overa finite field; in particular, when G is the group of F-points of a…
We consider special nonuntary represenation of the Iwasawa subgrouh with a nontrivial cohomology. For $p>2$ presunabley there are unitary representations with this property.
In this short article, we give a summary of the Sylow $p$-subgroups of the finite simple groups of classical Lie type.
In this note we collect some results on the deformation theory of toric Fano varieties.
The purpose of this second part of the series is to show a technical result on Chow groups of toric varieties. This is a crucial ingredient for the first part.
We describe the generalized Matsuda's theorem, and some results of a Burnside ring extend a partial Burnside ring. In particular, we give isomorphism between partial Burnside rings of different groups. Moreover, we consider the relationship…
We extend the notion of Poisson-Lie groups and Lie bialgebras from Poisson to g-quasi-Poisson geometry and provide a quantization to braided Hopf algebras in the corresponding Drinfeld category. The basic examples of these g-quasi-Poisson…
We prove several extensions of the Erdos-Fuchs theorem.
We prove the vanishing of certain low degree cohomologies of some induced representations. As an application, we determine certain low degree cohomologies of congruence groups.
It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…
An observation on Hall-Littlewood polynomials.
We prove the conjugacy of Sylow $p$-subgroups of linear pseudofinite groups under the assumption of the existence of a finite Sylow $p$-subgroup. We also give an example of a linear pseudofinite group with non-conjugate Sylow $2$-subgroups.