Reductions of integrable equations: dihedral group

We discuss the algebraic and analytic structure of rational Lax operators. With algebraic reductions of Lax equations we associate a reduction group - a group of automorphisms of the corresponding infinite-dimensional Lie algebra. We present a complete study of dihedral reductions for sl (2, ℂ) Lax operators with simple poles and corresponding integrable equations. In the last section we give three examples of dihedral reductions for sl (N, ℂ) Lax operators.