Lame operators with projective octahedral and icosahedral monodromies

Details Lame operators with projective octahedral and icosahedral monodromies Lame operators with projective octahedral and icosahedral monodromies

2004-11-08

arxiv.org/abs/math/0411159v2

Mathematics

Algebraic Geometry

23 pages, 34 figures; some spell-mistakes are fixed, and detailed explanations on the tables are added

Scientific paper

We show that there exists a Lame operator $L_n$ with projective octahedral monodromy for each $n\in{1/2}(\mathbf{N}+{1/2})\cup{1/3}(\mathbf{N}+{1/2}) $, and with projective icosahedral monodromy for each $n\in{1/3}(\mathbf{N}+{1/2})\cup{1/5}(\mathbf{N}+{1/2}) $. To this end, we construct Grothendieck's dessin d'enfants corresponding to the Belyi morphisms which pull-back hypergeometric operators into Lame operators $L_n$ with the desired monodromies.

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