Regge and Okamoto symmetries

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

References in corpus (4)

• Classical 6j-symbols and the tetrahedron
• Bäcklund Transformations of the Sixth Painlevé Equation in Terms of Riemann-Hilbert Correspondence
• Six results on Painleve VI
• 6j symbols for U_q(sl_2) and non-Euclidean tetrahedra

Cited by in corpus (9)

• Crossing Symmetry in Alpha Space
• Painlevé VI connection problem and monodromy of c=1 conformal blocks
• All-Mass $n$-gon Integrals in $n$ Dimensions
• Quivers and difference Painleve equations
• Multiplicity-free $U_q(s{l}_N)$ 6-j symbols: relations, asymptotics, symmetries
• Foliations on the moduli space of rank two connections on the projective line minus four points
• Singular modules for affine Lie algebras, and applications to irregular WZNW conformal blocks
• Projective Ponzano-Regge spin networks and their symmetries
• About integer-valued variants of the theta and 6j symbols