Related papers: Remarks on weak amalgamation and large conjugacy c…

We investigate the automorphism groups of $\aleph\_0$-categorical structures and prove that they are exactly the Roelcke precompact Polish groups. We show that the theory of a structure is stable if and only if every Roelcke uniformly…

We give a combinatorial description for the weak order on the hyperoctahedral group. This characterization is then used to analyze the order-theoretic properties of the shifted products of hyperoctahedral groups. It is shown that each…

Let $X$ be a Banach space and let $C$ be a closed convex bounded subset of $X$. It is proved that $C$ is weakly compact if, and only if, $C$ has the {it generic} fixed point property ($\mathcal{G}$-FPP) for the class of $L$-bi-Lipschitz…

Given a Polish group $G$, let $E(G)$ be the right coset equivalence relation $G^\omega/c(G)$, where $c(G)$ is the group of all convergent sequences in $G$. We first established two results: (1) Let $G,H$ be two Polish groups. If $H$ is TSI…

In 1999 V. Ivanov and S. Kerov observed that structure constants of algebras of conjugacy classes of symmetric groups $S_n$ admit a stabilization (in a non-obvious sense) as $n\to \infty$. We extend their construction to a class of pairs of…

We study the combinatorial equivalence of separable elements in types $A$ and $B$. A bijection is constructed from the set of separable permutations in the symmetric group $S_{n+1}$ to the set of separable signed permutations in the…

In this paper we discuss the structure of weighted weak Lebesgue spaces and weighted weak Orlicz spaces on $\mathbb{R}^n$. First, we present sufficient and necessary conditions for inclusion relation between weighted weak Lebesgue spaces.…

In this paper, we study the weak amenability of weighted measure algebras and prove that $M(G, \omega)$ is weakly amenable if and only if $G$ is discrete and every bounded quasi-additive function is inner. We also study the weak amenability…

Let (V,h) be a Hermitian space over a division algebra D which is of index at most two over a non-Archimedean local field k of residue characteristic not 2. Let G be the unitary group defined by h and let \sigma be the adjoint involution.…

We characterize completey (give a necessary and suffcient condition using special neat embeddings)for a relation algebra to belong to the amalgamation, strong amalgamation, and superamalgamation base of the class of representable algebras.…

This is the third in a series of four papers (with research announcement posted on this arXiv) that develop a decomposition theory for subgroups of $\text{Out}(F_n)$. In this paper, given an outer automorphism of $F_n$ and an…

The Ghahramani-Lau conjecture is established; in other words, the measure algebra of every locally compact group is strongly Arens irregular. To this end, we introduce and study certain new classes of measures (called approximately…

We establish connections between contact isometry groups of certain contact manifolds and compactly supported symplectomorphism groups of their symplectizations. We apply these results to investigate the space of symplectic embeddings of…

Let G be a reductive group over an algebraically closed field whose characteristic is not a bad prime for G. Let w be an elliptic element of the Weyl group which has minimal length in its conjugacy class. We show that there exists a unique…

We introduce the weak Haagerup property for locally compact groups and prove several hereditary results for the class of groups with this approximation property. The class contains a priori all weakly amenable groups and groups with the…

We study monoidal structures on the category of (co)modules over a weak bialgebra. Results due to Nill and Szlach\'anyi are unified and extended to infinite algebras. We discuss the coalgebra structure on the source and target space of a…

A compact space is said to be weakly Radon-Nikod\'{y}m (WRN) if it can be weak*-embedded into the dual of a Banach space not containing $\ell_1$. We investigate WRN Boolean algebras, i.e. algebras whose Stone space is WRN compact. We show…

Every fusion category C that is k-linear over a suitable field k, is the category of finite-dimensional comodules of a Weak Hopf Algebra H. This Weak Hopf Algebra is finite-dimensional, cosemisimple and has commutative bases. It arises as…

In a finite real reflection group, the reflection length of each element is equal to the codimension of its fixed space, and the two coincident functions determine a partial order structure called the absolute order. In complex reflection…

In this paper we investigate commuting involution graphs in classical affine Weyl groups. Let $W$ be a classical Weyl group of rank $n$, with $\tilde W$ its corresponding affine Weyl group. Our main result is that if $X$ is a conjugacy…