Introduction to middle convolution for differential equations with irregular singularities

We introduce middle convolution for systems of linear differential equations with irregular singular points, and we presend a tentative definition of the index of rigidity for them. Under some assumption, we show a list of terminal patterns of irreducible systems of linear differential equations by iterated application of middle convolution when the index is positive or zero.Comment: 24 page

On the Inozemtsev model

The BC_N Inozemtsev model is investigated. Finite-dimensional spaces which are invariant under the action of the Hamiltonian of the BC_N Inozemtsev model are introduced and it is shown that commuting operators of conserved quantities also preserve the finite-dimensional spaces. The BC_2 Inozemtsev model is studied in more detail.Comment: 6 pages, presented at the 12th Colloquium "Quantum Groups and Integrable Systems", Prague, June 12-14, 200