Lame operators with projective octahedral and icosahedral monodromies

2004/11/08 by Keiri Nakanishi, Nakanishi, Keiri
Mathematics · #14H30 #34G10 #Algebraic Geometry (math.AG) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AG #math.CA #msc:14H30 #msc:34G10

paper · pdf · doi:10.48550/arxiv.math/0411159

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

arxiv created 2004/11/18 · arxiv updated 2009/12/01

Abstract

We show that there exists a Lame operator L_n 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 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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