Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 16, pages 245--261.
Asymptotics and 6j-symbols
Justin Roberts
Abstract.
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.
Keywords.
6j-symbol, asymptotics, quantization
AMS subject classification.
Primary: 22E99.
Secondary: 81R05, 51M20.
E-print: arXiv:math.QA/0201177
Submitted to GT on 19 December 2001.
(Revised 1 August 2002.)
Paper accepted 10 September 2002.
Paper published 13 October 2002.
Notes on file formats
Justin Roberts
Department of Mathematics, UC San Diego
9500 Gilman Drive, La Jolla, CA 92093, USA
Email: justin@math.ucsd.edu
GTM home page
