2002/01/31 by Justin Roberts · 1 citation
Mathematics · Physics and Astronomy · #math.QA #math-ph #math.MP #msc:22E99 #msc:81R05 #msc:51M20
published as Geom. Topol. Monogr. 4 (2002) 245-261 · Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper16.abs.html
arxiv created 2002/10/15 · arxiv updated 2009/11/30
Recent interest in the Kashaev-Murakami-Murakami hyperbolic volume conjecture has made it seem important to be able to understand the asymptotic behaviour of certain special functions arising from representation theory -- for example, of the quantum 6j-symbols for SU(2). In 1998 I worked out the asymptotic behaviour of the classical 6j-symbols, proving a formula involving the geometry of a Euclidean tetrahedron which was conjectured by Ponzano and Regge in 1968. In this note I will try to explain the methods and philosophy behind this calculation, and speculate on how similar techniques might be useful in studying the quantum case.