Related papers: Normal Reflection Subgroups of Complex Reflection …

Let $\Gamma$ be a discrete group acting by isometries on a product $X=X_1\times X_2$ of Hadamard spaces. We further require that $X_1$, $X_2$ are locally compact and $\Gamma$ contains two elements projecting to a pair of independent rank…

We show that if a group contains $\mathbb{Z}^n \times F_m$ as a finite-index subgroup, then its cogrowth series is the diagonal of a rational function for every generating set. This answers a question of Pak and Soukup on the cogrowth of…

The central concept in the harmonic analysis of a compact group is the completeness of Peter-Weyl orthonormal basis as constructed from the matrix coefficients of a maximal set of irreducible unitary representations of the group, leading…

The basic theory of semi-measures on locally compact Abelian groups is extended to prove the existence of a generalised Eberlein decomposition into such semi-measures.

A p-local finite group is an algebraic structure with a classifying space which has many of the properties of p-completed classifying spaces of finite groups. In this paper, we construct a family of 2-local finite groups, which are exotic…

We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…

A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…

The Steinberg tensor product theorem is a fundamental result in the modular representation theory of reductive algebraic groups. It describes any finite-dimensional simple module of highest weight $\lambda$ over such a group as the tensor…

An important combinatorial result in equivariant cohomology and $K$-theory Schubert calculus is represented by the formulas of Billey and Graham-Willems for the localization of Schubert classes at torus fixed points. These formulas work…

The object of this paper is to find a necessary and sufficient condition for the groups $G_1, G_2, ..., G_n$ so that every normal subgroup of the product $\prod_{i=1}^{n} G_i$ is of the type $\prod_{i=1}^{n} N_i$ with $N_i \trianglelefteq…

Suppose that G is a finite, unitary reflection group acting on a complex vector space V and X is the fixed point subspace of an element of G. Define N to be the setwise stabilizer of X in G, Z to be the pointwise stabilizer, and C=N/Z. Then…

We describe the structure of Sylow {\ell}-subgroups of a finite reduc-tive group G(Fq) when q $\not\equiv$ 0 (mod {\ell}) that we find governed by a complex reflection group attached to G and {\ell}, which depends on {\ell} only through the…

Given a number field $k$, we show that, for many finite groups $G$, all the Galois extensions of $k$ with Galois group $G$ cannot be obtained by specializing any given finitely many Galois extensions $E/k(T)$ with Galois group $G$ and $E/k$…

Originally motivated by questions of P. Etingof related to growth rates of tensor powers in symmetric tensor categories, we obtain general bounds on the order of finite subgroups of ${\rm GL}(n,\mathbb{C})$ with restricted composition…

We define a new class of generating function transformations related to polylogarithm functions, Dirichlet series, and Euler sums. These transformations are given by an infinite sum over the $j^{th}$ derivatives of a sequence generating…

The structure of extended affine Weyl symmetry group of higher Painlev\'e equations of $N$ periodicity depends on whether $N$ is even or odd. We find that for even $N$, the symmetry group ${\widehat A}^{(1)}_{N-1}$ contains the conventional…

We establish a criterion for the strong $F$-regularity of a (non-Gorenstein) Cohen-Macaulay reduced complete local ring of dimension at least $2$, containing a perfect field of prime characteristic $p$. We also describe an explicit…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

For the second fundamental representation of the general linear group over a commutative ring $R$ we construct straightforward and uniform polynomial expressions of elementary generators as products of elementary conjugates of an arbitrary…

Let $k$ be a finitely generated field, let $X$ be an algebraic variety and $G$ a linear algebraic group, both defined over $k$. Suppose $G$ acts on $X$ and every element of a Zariski-dense semigroup $\Gamma \subset G(k)$ has a rational…