On the Riemann–Hilbert problem for linear q-difference systems

The talk concerns with the Birkhoff theory of linear q-difference systems. I will tell about solutions and the monodromy matrix in the q-difference case. There will be formulated an analog of the Riemann–Hilbert problem and Birkhoff's result. Then it will be explained how the latter can be refined in the case when all the pairwise differences of zeros of the determinant of the coefficient matrix are not integer numbers.