Special functions: Group-theoretical aspects and applications

Ends—group Theoretical and Topological Aspects

This is a survey of topological, group theoretical and some graph theoretical aspects of ends. After discussing the notion of ends in topology, we consider ends of graphs and show that the metric end topology of connected graphs is metrizable. The “1–2–Cantor theorem” is proved for graphs whose ends are all limit ends, that is, ends which are accumulation points of an orbit of the group of auto...

S29. Special functions, orthogonal polynomials and applications

Laguerre-type operators, Special functions and Applications

The monomiality principle was introduced (see e.g. [1] and the references therein) in order to derive properties of special polynomials from the corresponding ones holding for monomials. A set of paramount importance in this framework is given by the Hermite-Kampé de Fériet (shortly H-KdF) or Gould-Hopper polynomials [2], [3], [4]. As it is well known, the Hermite-Kampé de Fériet polynomials H ...

Group-Theoretical Aspects of Orbifold and Conifold GUTs

Motivated by the simplicity and direct phenomenological applicability of field-theoretic orbifold constructions in the context of grand unification, we set out to survey the immensely rich group-theoretical possibilities open to this type of model building. In particular, we show how every maximal-rank, regular subgroup of a simple Lie group can be obtained by orbifolding and determine under wh...

Group Signatures: Better Efficiency and New Theoretical Aspects

A group signature scheme allows members of a group to sign messages anonymously. To counter misuse, the so-called group manager can revoke the anonymity. This paper contributes two results to the area of group signatures. First, we improve the state-of-theart scheme by Ateniese et al. by an order of magnitude. Our new scheme satisfies the recent security definition by Bellare et al. Second, and...