Related papers: Reduction for flag-transitive symmetric designs wi…

We give a new interpretation and proof of the "quasi-particle" type character formulas for integrable representations of the simply-laced affine Kac-Moody algebras through a new "semi-infinite" construction of such representations. We…

This paper initiates the investigation of the family of $(G,s)$-geodesic-transitive digraphs with $s\geq 2$. We first give a global analysis by providing a reduction result. Let $\Gamma$ be such a digraph and let $N$ be a normal subgroup of…

We define, for any group $G$, finite approximations ; with this tool, we give a new presentation of the profinite completion $\hat{\pi} : G \to \hat{G}$ of an abtract group $G$. We then prove the following theorem : if $k$ is a finite prime…

A finite graph $\Gamma$ is called $G$-symmetric if $G$ is a group of automorphisms of $\Gamma$ which is transitive on the set of ordered pairs of adjacent vertices of $\Gamma$. We study a family of symmetric graphs, called the unitary…

Let $\Omega=\{1,2,...,n\}$ where $n \ge 2$. The {\em shape} of an ordered set partition $P=(P_1,..., P_k)$ of $\Omega$ is the integer partition $\lambda=(\lambda_1,...,\lambda_k)$ defined by $\lambda_i = |P_i|$. Let G be a group of…

We provide a Lagrangian construction for the fixed-point subalgebra, together with its idempotent form, in a quasi-split symmetric pair of type $A_{n-1}$. This is obtained inside the limit of a projective system of Borel-Moore homologies of…

We study point-block incidence structures $(\mathcal{P},\mathcal{B})$ for which the point set $\mathcal{P}$ is an $m\times n$ grid. Cameron and the fourth author showed that each block $B$ may be viewed as a subgraph of a complete bipartite…

We refer to $d(G)$ as the minimal cardinality of a generating set of a finite group $G$, and say that $G$ is $d$-generated if $d(G)\leq d$. A transitive permutation group $G$ is called $\frac{3}{2}$-transitive if a point stabilizer…

Let $\Gamma$ be a $G$-symmetric graph with vertex set $V$. We suppose that $V$ admits a $G$-partition $\mathcal{B} = \{ B_0, ... , B_b \}$, with parts of size $v$, and that the quotient graph induced on $\mathcal B$ is a complete graph of…

Let X be a compact Kaehler manifold of complex dimension n. Let G be a connected solvable subgroup of the automorphism group Aut(X), and let N(G) be the normal subgroup of G of elements of null entropy. One of the goals of this paper is to…

The classical result of Eisenhart states that if a Riemannian metric $g$ admits a Riemannian metric that is not constantly proportional to $g$ and has the same (parameterized) geodesics as $g$ in a neighborhood of a given point, then $g$ is…

The $k$-th token graph of a graph $G=(V,E)$ is the graph $F_k(G)$ whose vertices are the $k$-subsets of $V$ and whose edges are all pairs of $k$-subsets $A,B$ such that the symmetric difference of $A$ and $B$ forms an edge in $G$. Let…

In this paper, we examine the structure of vertex- and edge-transitive strongly regular graphs, using normal quotient reduction. We show that the irreducible graphs in this family have quasiprimitive automorphism groups, and prove (using…

Suppose that a finite group $G$ admits an automorphism $\varphi $ of order $2^n$ such that the fixed-point subgroup $C_G(\varphi ^{2^{n-1}})$ of the involution $\varphi ^{2^{n-1}}$ is nilpotent of class $c$. Let $m=|C_G(\varphi)|$ be the…

Let $\pi : X\to \Lambda$ be a flat family of smooth complex projective varieties parameterized by a smooth quasi-projective variety $\Lambda$, and let $f: X\to X$ be a family of automorphisms with positive topological entropy. Suppose…

We investigate the critical properties of the three-dimensional (3D) antiferromagnetic RP(N-1}) model, which is characterized by a global O(N) symmetry and a discrete Z_2 gauge symmetry. We perform a field-theoretical analysis using the…

The distinguishing index $D'(\Gamma)$ of a graph $\Gamma$ is the least number $k$ such that $\Gamma$ has an edge-coloring with $k$ colors preserved only by the trivial automorphism. In this paper we prove that if the automorphism group of a…

The notions of symbolic matrix system and $\lambda$-graph system for a subshift are generalizations of symbolic matrix and $\lambda$-graph (= finite symbolic matrix) for a sofic shift respectively ([Doc. Math. 4(1999), 285-340]). M. Nasu…

We prove the semisimplicity conjecture for A-motives over finitely generated fields K. This conjecture states that the rational Tate modules V_p(M) of a semisimple A-motive M are semisimple as representations of the absolute Galois group of…

We prove that an arbitrary compact metrizable group can be realized as the automorphism group of a graphing; this is a continuous analogue to Frucht's theorem recovering arbitrary finite groups are automorphism groups of finite graphs. The…