Stokes factors and multilogarithms

Details Stokes factors and multilogarithms Stokes factors and multilogarithms

2010-06-23

arxiv.org/abs/1006.4623v6

Mathematics

Classical Analysis and ODEs

final version, to appear in Crelle's journal. arXiv admin note: text overlap with arXiv:0801.3974

Scientific paper

Let G be a complex, affine algebraic group and D a meromorphic connection on the trivial G-bundle over P^1, with a pole of order 2 at zero and a pole of order 1 at infinity. We show that the map S taking the residue of D at zero to the corresponding Stokes factors is given by an explicit, universal Lie series whose coefficients are multilogarithms. Using a non-commutative analogue of the compositional inversion of formal power series, we show that the same holds for the inverse of S, and that the corresponding Lie series coincides with the generating function for counting invariants in abelian categories constructed by D. Joyce.

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