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.

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Justin Roberts
Department of Mathematics, UC San Diego
9500 Gilman Drive, La Jolla, CA 92093, USA
Email: justin@math.ucsd.edu

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