Regge and Okamoto symmetries

Details Regge and Okamoto symmetries Regge and Okamoto symmetries

2006-03-16

arxiv.org/abs/math/0603398v1

Comm. Math. Phys. 276 (2007), no. 1, 117-130

Mathematics

Representation Theory

14 pages

Scientific paper

10.1007/s00220-007-0328-x

We will relate the surprising Regge symmetry of the Racah-Wigner 6j symbols to the surprising Okamoto symmetry of the Painleve VI differential equation. This then presents the opportunity to give a conceptual derivation of the Regge symmetry, as the representation theoretic analogue of the author's previous derivation of the Okamoto symmetry. [The resulting derivation is quite simple, so it would be surprising if it has not been previously observed. Any references would be appreciated!]

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