Lamé operators with projective octahedral and icosahedral monodromies
نویسنده
چکیده
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 monodromies.
منابع مشابه
Algebraic Solutions of the Lamé Equation, Revisited
A minor error in the necessary conditions for the algebraic form of the Lamé equation to have a finite projective monodromy group, and hence for it to have only algebraic solutions, is pointed out. [See F. Baldassarri, “On algebraic solutions of Lamé’s differential equation”, J. Differential Equations 41 (1) (1981), 44–58.] It is shown that if the group is the octahedral group , then the degree...
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