Related papers: On Kazhdan's property (T) for isotropic reductive …

In a recent article, D. Kazhdan and A. Yom Din conjectured the validity of an asymptotic form of Schur's orthogonality for tempered irreducible unitary representations of semisimple groups defined over local fields. In the non-Archimedean…

In this article we define a set of matrices analogous to Vaserstein-type matrices which was introduced in the paper `Serre's problem on projective modules over polynomial rings and algebraic K-theory' by Suslin-Vaserstein in 1976. We prove…

We construct several series of explicit presentations of infinite hyperbolic groups enjoying Kazhdan's property (T). Some of them are significantly shorter than the previously known shortest examples. Moreover, we show that some of those…

The paper is devoted to model-theoretic properties of Kac-Moody groups with the focus on elementary equivalence of Kac-Moody groups. We show that elementary equivalence of (untwisted) affine Kac-Moody groups implies coincidence of their…

We study reductive subgroups $H$ of a reductive linear algebraic group $G$ -- possibly non-connected -- such that $H$ contains a regular unipotent element of $G$. We show that under suitable hypotheses, such subgroups are $G$-irreducible in…

For a finite group acting on a polynomial ring, the Chevalley-Shephard-Todd Theorem proves that the fixed subring is isomorphic to a polynomial ring if and only if the group is generated by pseudo-reflections. In recent years, progress was…

The main result of this paper is a generalization of the theorem of Chevalley-Shephard-Todd to the rings of invariants of pseudoreflection groups over Dedekind domains. In the special case of a principal ideal domain in which the group…

We construct the first examples of infinite sharply 2-transitive groups which are finitely generated. Moreover, we construct such a group that has Kazhdan property (T), is simple, has exactly four conjugacy classes, and we show that this…

The Grothendieck--Serre conjecture predicts that every generically trivial torsor under a reductive group over a regular semilocal ring is itself trivial. Extending the work of \v{C}esnavi\v{c}ius and Fedorov, we prove a non-noetherian…

We formulate and prove relative versions of several classical decompositions known in the theory of Chevalley groups over commutative rings. As an application we obtain upper estimates for the width of principal congruence subgroups in…

Let $G$ be the linear algebraic group $SL_3$ over a field $k$ of characteristic two. Let $A$ be a finitely generated commutative $k$-algebra on which $G$ acts rationally by $k$-algebra automorphisms. We show that the full cohomology ring…

It was conjectured by H. Zassenhaus that a torsion unit of an integral group ring of a finite group is conjugate to a group element within the rational group algebra. The object of this note is the computational aspect of a method developed…

We introduce and study the class of groups graded by root systems. We prove that if {\Phi} is an irreducible classical root system of rank at least 2 and G is a group graded by {\Phi}, then under certain natural conditions on the grading,…

In his seminal paper on complex reflection arrangements, Bessis introduces a Garside structure for the braid group of a well-generated irreducible complex reflection group. Using this Garside structure, he establishes a strong connection…

In this paper, we prove two structure theorems for twisted Chevalley groups $G_\sigma (R)$ over a commutative ring $R$ with unity. The first theorem concerns the normality of $E'_\sigma (R,J)$, the elementary congruence subgroups at level…

We begin to study model-theoretic properties of non-split isotropic reductive group schemes. In this paper we show that the base ring $K$ is e-interpretable in the point group $G(K)$ of every sufficiently isotropic reductive group scheme…

We classify all compactly generated t-structures in the unbounded derived category of an arbitrary commutative ring, generalizing the result of [ATLJS10] for noetherian rings. More specifically, we establish a bijective correspondence…

The purpose of this article is to give, for any commutative ring A, an explicit minimal set of generators for the ring of multisymmetric functions TS^d_A(A[x_1,...,x_r]) as an A-algebra. In characteristic zero, i.e. when A is an algebra…

Let $\Phi$ be a reduced irreducible root system of rank $\ge 2$, let $R$ be a commutative ring and let $I,J$ be two ideals of $R$. In the present paper we describe generators of the commutator groups of relative elementary subgroups…

We extend (scheme-theoretic) Bruhat-Tits theory to quasi-reductive groups i.e. with trivial split unipotent radical over discretely valued henselian non-archimedean fields $K$, whose ring of integers is excellent and residue field is…