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

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