Partial indices of a matrix Riemann problem on the torus (Q5966241)

The authors study the n-dimensional Riemann problem on the torus \((T)\quad u^ 2=\prod^{2}_{j-1}(z-a_ j)(z-b_ j)\) with boundary condition \((1)\quad\Phi^+(t,v)=\Omega (t,v)\Phi^-(t,v);\quad (t,v)\in L\) given on a curve \(L\subset T\), composed from n-1 pieces of disjoint arcs \(L_ k\), without selfcrossings. With an appropriate regularity condition at \(\infty\), the authors obtain the canonical matrix of solutions for the problem (1) when \(\Omega_ k=\Omega_{/L_ k}=(\Omega_ 1)^ k\) with \(\Omega_ 1\) the matrix of the permutation \(\left( \begin{matrix} 1,2,...,n\\ 2,3,...,n,1\end{matrix} \right).\) They also give formulae for the partial indices.