Regge and Okamoto symmetries
Philip Boalch
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!]
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