Unitary monodromy of Lamé differential operators
نویسنده
چکیده
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.
منابع مشابه
Lamé operators with projective octahedral and icosahedral monodromies
We show that there exists a Lamé operator Ln with projective octahedral monodromy for each n ∈ 1 2 (N + 1 2 ) ∪ 1 3 (N + 1 2 ), and with projective icosahedral monodromy for each n ∈ 1 3 (N+ 1 2 )∪ 1 5 (N+ 1 2 ). To this end, we construct Grothendieck’s dessins d’enfants corresponding to the Belyi morphisms which pull-back hypergeometric operators into Lamé operators Ln with the desired monodro...
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