Asymptotics and 6j-symbols

Details Asymptotics and 6j-symbols Asymptotics and 6j-symbols

2002-01-18

arxiv.org/abs/math/0201177v2

Geom. Topol. Monogr. 4 (2002) 245-261

Mathematics

Quantum Algebra

Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon4/paper16.abs.html

Scientific paper

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.

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