Unitary monodromy of Lamé differential operators

Abstract

The classical second order Lamé equation contains a so-called accessory parameter B. In this paper we study for which values of B the Lamé equation has a monodromy group which is conjugate to a subgroup of SL(2,R) (unitary monodromy with indefinite hermitian form). We refomulate the problem as a spectral problem and give an asymptotic expansion for the spectrum. - To be published in Regular and Chaotic Dynamics, 12, 6, 630-641, special issue in honor of Richard Cushman, 2007.