Regge and Okamoto symmetries
arXiv:math/0603398 · doi:10.1007/s00220-007-0328-x
Abstract
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!]
14 pages