Regge and Okamoto symmetries

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!]Comment: 14 page

Stability conditions and Stokes factors

Let A be the category of modules over a complex, finite-dimensional algebra. We show that the space of stability conditions on A parametrises an isomonodromic family of irregular connections on P^1 with values in the Hall algebra of A. The residues of these connections are given by the holomorphic generating function for counting invariants in A constructed by D. Joyce.Comment: Very minor changes. Final version. To appear in Inventione

Symplectic geometry and isomonodromic deformations

SIGLEAvailable from British Library Document Supply Centre-DSC:D206148 / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Symplectic geometry and isomonodromic deformations

SIGLEAvailable from British Library Document Supply Centre-DSC:D206148 / BLDSC - British Library Document Supply CentreGBUnited Kingdo