Related papers: From Anderson to Zeta

Let $\Gamma$ be a Coxeter graph, let $W$ be its associated Coxeter group, and let $G$ be a group of symmetries of $\Gamma$.Recall that, by a theorem of H{\'e}e and M\"uhlherr, $W^G$ is a Coxeter group associated to some Coxeter graph $\hat…

We investigate the class of root systems $R$ obtained by extending an $A_1$-type irreducible root system by a free abelian group $G$. In this context there is a Weyl group $W$ and a group $U$ with the presentation by conjugation. Both…

We investigate the local topological structure of non-metrizable topological groups through the lens of Tukey order and cofinal types. Motivated by recent advances in topological groups admitting an $\omega^\omega$-base, we introduce the…

Let $\bH$ be the generic Iwahori--Hecke algebra associated with a finite Coxeter group $W$. Recently, we have shown that $\bH$ admits a natural cellular basis in the sense of Graham--Lehrer, provided that $W$ is a Weyl group and all…

We find an explicit $S_n$-equivariant bijection between the integral points in a certain zonotope in $\mathbb{R}^n$, combinatorially equivalent to the permutahedron, and the set of $m$-parking functions of length $n$. This bijection…

We continue the study of separable elements in finite Weyl groups. These elements generalize the well-studied class of separable permutations. We show that the multiplication map $W/U \times U \to W$ is a length-additive bijection, or…

Let $x$ be an eigenvector for an element of a finite irreducible reflection group $W$. Let $W_x$ denote the subgroup of $W$ which stabilises $x$. We provide an upper bound for the number of roots in the root system of $W_x$ . This…

Let $(W,S)$ be a Coxeter system whose graph is connected, with no infinite edges. A self-map $\tau$ of $W$ such that $\tau_{\sigma\theta}\in \{\tau_{\theta},\ \sigma\tau_{\theta}\}$ for all $\theta\in W$ and all reflections $\sigma$…

For a prime number $p$ and any natural number $n$ we introduce, by giving an explicit recursive formula, the $p$-Jones-Wenzl projector ${}^p\operatorname{JW}_n$, an element of the Temperley-Lieb algebra $TL_n(2)$ with coefficients in…

For any irreducible real reflection group $W$ with Coxeter number $h$, Armstrong, Reiner, and the author introduced a pair of $W \times \ZZ_h$-modules which deserve to be called {\sf $W$-parking spaces} which generalize the type A notion of…

A finite Coxeter group $W$ has a natural metric $d$ and if $\mathcal{M}$ is a subset of $W$, then for each $u\in W$, there is $q\in \mathcal{M}$ such that $d(u,q)=d(u,\mathcal{M})$. Such $q$ is not unique in general but if $\mathcal{M}$ is…

Let $(W,S)$ be a Coxeter system, $S$ finite, and let $G_{W}$ be the associated Artin group. One has configuration spaces $Y,\ Y_{W},$ where $G_{W}=\pi_1(Y_{W}),$ and a natural $W$-covering $f_{W}:\ Y\to Y_{W}.$ The Schwarz genus $g(f_{W})$…

An affine Hecke algebra H contains a large abelian subalgebra A. The center Z of H is the subalgebra of Weyl group invariant elements in A. The natural trace of the affine Hecke algebra can be written as an integral of a rational $n$ form…

Given an open, bounded, planar set $\Omega$, we consider its $p$-Cheeger sets and its isoperimetric sets. We study the set-valued map $\mathfrak{V}:[\frac12,+\infty)\rightarrow\mathcal{P}((0,|\Omega|])$ associating to each $p$ the set of…

This article presents a unified bijective scheme between planar maps and blossoming trees, where a blossoming tree is defined as a spanning tree of the map decorated with some dangling half-edges that enable to reconstruct its faces. Our…

Let R be an associative ring with identity. We study an elementary generalization of the classical Zariski topology, applied to the set of isomorphism classes of simple left R-modules (or, more generally, simple objects in a complete…

Stone locales together with continuous maps form a coreflective subcategory of spectral locales and perfect maps. A proof in the internal language of an elementary topos was previously given by the second-named author. This proof can be…

We introduce and study integral planes associated with crystallographic and non-crystallographic integral systems in real composition algebras. For an integral order $\Order$ in such an algebra we define the plane $\Order^{2}$ with…

The Iwahori-Hecke algebra $\mathcal{H}$ of a Coxeter system $(W,S)$ has a "standard basis" indexed by the elements of $W$ and a "bar involution" given by a certain antilinear map. Together, these form an example of what Webster calls a…

Let A_E be the canonical AF subalgebra of a graph C*-algebra C*(E) associated with a locally finite directed graph E. For Brown-Voiculescu's topological entropy ht(\Phi_E) of the canonical completely positive map \Phi_E on C*(E),…