The effective action on an orbifolded sphere is computed for minimally coupled scalar fields. The results are presented in terms of derivatives of Barnes ζ–functions and it is shown how these may be evaluated. Numerical values are shown. An analytical, heat-kernel derivation of the Cesàro-Fedorov formula for the number of symmetry planes of a regular solid is also presented. 1 1. Introduction. ...

Using a generalized spherical mean operator, we obtain the generalizationof Titchmarsh's theorem for the Dunkl transform for functions satisfyingthe Lipschitz condition in L2(Rd;wk), where wk is a weight function invariantunder the action of an associated reection groups.

In a Cayley digraph on a group G, if a distinct colour is assigned to each arc-orbit under the left-regular action of G, it is not hard to show that the elements of the left-regular action of G are the only digraph automorphisms that preserve this colouring. In this paper, we show that the equivalent statement is not true in the most straightforward generalisation to G-vertex-transitive digraph...

This note is part of a general programme to classify the automorphism groups of finite linear spaces. There have been a number of contributions to this programme, including two recent surveys [8, 3]. One of the most significant contributions was the classification of flag-transitive linear spaces [2]. Since then, the effort has been to classify the line-transitive examples. These fall naturally...

The following problem is considered: when can the action of a cancellative semigroup S on a set be extended to a simply transitive action of the universal group of S on a larger set.

There is a familiar construction with two finite, transitive permutation groups as input and a finite, transitive permutation group, called their wreath product, as output. The corresponding 'imprimitive wreath decomposition concept is the first subject of this paper. A formal definition is adopted and an overview obtained for all such decompositions of any given finite, transitive group. The r...

A graph is said to be half-arc-transitive if its automorphism group acts transitively on the set of its vertices and edges but not on the set of its arcs. With each half-arc-transitive graph of valency 4 a collection of the so called alternating cycles is associated, all of which have the same even length. Half of this length is called the radius of the graph in question. Moreover, any two adja...

An automorphism of a 7nite simple graph is an adjacency automorphism if for every vertex x∈V ( ), either x = x or x is adjacent to x in . An adjacency automorphism 7xing no vertices is a shift. A connected graph is strongly adjacency-transitive (respectively, uniquely shift-transitive) if there is, for every pair of adjacent vertices x; y∈V ( ), an adjacency automorphism (respectively, a unique...

Abstract Let $Z$ be a unimodular real spherical space. We develop theory of constant terms for tempered functions on $Z$, which parallels the work Harish-Chandra. The $f_I$ an eigenfunction $f$ are parametrized by subsets $I$ set $S$ roots that determine fine geometry at infinity. Constant transitive i.e., $(f_J)_I=f_I$ $I\subset J$, and our main result is quantitative bound difference $f-f_I$,...

We classify trivalent vertex-transitive graphs whose edge sets have a partition into 2-factor composed of two cycles and 1-factor that is invariant under the action automorphism group.