1999/02/18 by T. Gannon, TERRY GANNON · 2 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #hep-th #math.QA #msc:17B67 #msc:81R10 #msc:81T40
paper · pdf · doi:10.1142/s0129055x00000265
published as Rev.Math.Phys. 12 (2000) 739-748 · 10 pages, plain tex; an historical remark on A-D-E corrected, 2 references added, several new comments added to conclusion
arxiv created 1999/02/18 · openalex publication_date 2000/05/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In 1986 Cappelli, Itzykson and Zuber classified all modular invariant partition functions for the conformal field theories associated to the affine A 1 algebra; they found they fall into an A-D-E pattern. Their proof was difficult and attempts to generalise it to the other affine algebras failed — in hindsight the reason is that their argument ignored most of the rich mathematical structure present. We give here the "modern" proof of their result; it is an order of magnitude simpler and shorter, and much of it has already been extended to all other affine algebras. We conclude with some remarks on the A-D-E pattern appearing in this and other RCFT classifications.