Moscow-Petersburg seminar on Low-dimensional mathematics
April 16, 2004

S.K.Duzhin
On the ratio of two particular solutions of a certain ordinary differential
equation

The Drinfeld associator Phi is a an series in two non-commuting variables A
and B which can be defined as the ratio of two special solutions of the
Knizhnik-Zamolodchikov equation G'(z)=(A/z+B/(z-1))G(z). Using iterated
integrals one can obtain an explicit formula expressing the coefficients
of the associator through the multiple zeta values zeta(a_1,...,a_k)
=sum_{n_1>=...>=n_k>1} n_1^{-a_1}*...*n_k^{-a_k}.
This formula is, however, very cumbersome and so is of little help in
understanding the structure of the associator. In this talk we suggest a
direction towards a compact and meaningful formula for the associator and
do some first steps in this direction.


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