Geometry & Topology Monographs, Vol. 4 (2002),
Invariants of knots and 3-manifolds (Kyoto 2001),
Paper no. 16, pages 245--261.
Asymptotics and 6j-symbols
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.
6j-symbol, asymptotics, quantization
AMS subject classification.
Secondary: 81R05, 51M20.
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
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