arXiv subjects

A. Coste

Publications and source records attributed to A. Coste.

4 recordsLinked to original sources

arXiv2003

Representation Theory of Twisted Group Double

This text collects useful results concerning the quasi-Hopf algebra $\D $. We give a review of issues related to its use in conformal theories and physical mathematics. Existence of such algebras based on 3-cocycles with values in $ {R} / {Z} $ which mimic for finite groups Chern-Simons terms of gauge theories, open wide perspectives in the so called "classification program". The modularisation theorem proved for quasi-Hopf algebras by two authors some years ago makes the computation of topological invariants possible. An updated, although partial, bibliography of recent developments is provided.

hep-th↗

arXiv2000

Finite Group Modular Data

In a remarkable variety of contexts appears the modular data associated to finite groups. And yet, compared to the well-understood affine algebra modular data, the general properties of this finite group modular data has been poorly explored. In this paper we undergo such a study. We identify some senses in which the finite group data is similar to, and different from, the affine data. We also consider the data arising from a cohomological twist, and write down, explicitly in terms of quantities associated directly with the finite group, the modular S and T matrices for a general twist, for what appears to be the first time in print.

hep-th↗

arXiv1999

Congruence subgroups and rational conformal field theory

We address here the question of whether the characters of an RCFT are modular functions for some level N, i.e. whether the representation of the modular group SL_2(Z) coming from any RCFT is trivial on some congruence subgroup. We prove that if the matrix T, associated to $(\matrix{1&1\cr 0&1})\in{\rm SL}_2(\Z)$, has ODD order, then this must be so. When the order of T is even, we present a simple test which if satisfied -- and we conjecture it always will be -- implies that the characters for that RCFT will also be level N. We use this to explain three curious observations in RCFT made by various authors.

math.QA↗

arXiv1996

Comments on the Links between su(3) Modular Invariants, Simple Factors in the Jacobian of Fermat Curves, and Rational Triangular Billiards

We examine the proposal made recently that the su(3) modular invariant partition functions could be related to the geometry of the complex Fermat curves. Although a number of coincidences and similarities emerge between them and certain algebraic curves related to triangular billiards, their meaning remains obscure. In an attempt to go beyond the su(3) case, we show that any rational conformal field theory determines canonically a Riemann surface.

hep-th↗