Related papers: The Berenstein-Kirillov group and cactus groups

In this paper we identify QD(A,B), the quasidiagonal classes in KK_1(A,B), in terms of K_*(A) and K_*(B), and we use these results in various applications. Here is our central result. Theorem: Suppose that A is in the category of separable…

Our goal is to find classes of convolution semigroups on Lie groups $G$ that give rise to interesting processes in symmetric spaces $G/K$. The $K$-bi-invariant convolution semigroups are a well-studied example. An appealing direction for…

When a discrete group admits a convex-cocompact action on a non-compact rank-one symmetric space, there is a natural lower bound for the Hausdorff dimension of the limit set, given by the Ahlfors regular conformal dimension of the boundary…

We introduce a new notion of twisted actions of inverse semigroups and show that they correspond bijectively to certain regular Fell bundles over inverse semigroups, yielding in this way a structure classification of such bundles. These…

We introduce and study the notion of continuous orbit equivalence of actions of countable discrete groups on Cartan pairs in (twisted) groupoid context. We characterize orbit equivalence of actions in terms of the corresponding…

We construct a group acting on a binary rooted tree; this discrete group mimics the monodromy action of iterates of $f(z)=z^2-1$ on associated coverings of the Riemann sphere. We then derive some algebraic properties of the group, and…

We exhibit an obstruction for groups with Relative Property (T) to act on the real line by bi-Lipschitz homeomorphisms. This condition is expressed in terms of the Lipschitz and Kazhdan constants associated to finite generating subsets. As…

We examine the relationship between the actions of two Weyl groups on the cohomology of a smooth quiver variety: the Maffei's action of the Weyl group associated to the quiver, and the symplectic Springer action of the Namikawa-Weyl group…

Let $(W,S)$ be a Coxeter system, let $\varphi$ be a weight function on $S$ and let ${\mathrm{Cact}}\_W$ denote the associated {\it cactus group}. Following an idea of I. Losev, we construct an action of ${\mathrm{Cact}}\_W \times…

We prove the Kazhdan-Lusztig correspondence for a class of vertex operator superalgebras which, via the work of Costello-Gaiotto, arise as boundary VOAs of topological B twist of 3d $\mathcal{N}=4$ abelian gauge theories. This means that we…

We introduce a new notion of rank for unitary representations of semisimple groups over a local field of characteristic zero. The theory is based on Kirillov's method of orbits for nilpotent groups over local fields. When the semisimple…

We investigate two Galois connection between the congruence lattice and the lattice of subgroups of the displacement group of left quasigroups. Such connections were already studied for racks and quandles. We introduce the class of left…

We introduce crossingless sheaves in certain equivariant derived categories which are analogous to the Bezrukavnikov-Mirkovic exotic sheaves for two-block nilpotents. We calculate the classes of crossingless sheaves in equivariant K-theory…

We study the duality group of $\hat{A}_{n-1}$ quiver gauge theories, primarily using their M5-brane construction. For $\mathcal{N}=2$ supersymmetry, this duality group was first noted by Witten to be the mapping class group of a torus with…

We introduce a bivariant version of the Cuntz semigroup as equivalence classes of order zero maps generalizing the ordinary Cuntz semigroup. The theory has many properties formally analogous to KK-theory including a composition product. We…

We classify a large class of Z^2-actions on the Kirchberg algebras employing the Kasparov group KK^1 as the space of classification invariants.

We build actions of Thompson group V (related to the Cantor set) and of the so-called "spheromorphism" group of Neretin, on "towers" of moduli spaces of genus zero real stable curves. The latter consist of inductive limits of spaces which…

In this paper we study the classes of superconnected and superfaithful left quasigroups, that are relevant in the study of Mal'cev varieties of left quasigroups \cite{Maltsev_paper}. Then we focus on quandles and in particular to the…

A group-category is an additively semisimple category with a monoidal product structure in which the simple objects are invertible. For example in the category of representations of a group, 1-dimensional representations are the invertible…

We develop an analogy between right-angled Artin groups and mapping class groups through the geometry of their actions on the extension graph and the curve graph respectively. The central result in this paper is the fact that each…