MR2761092
Yoshishige HARAOKA and Mitsuo KATO
Yoshishige HARAOKA and Mitsuo KATO
Generating Systems for Finite Irreducible Complex Reflection Groups
Funkcialaj Ekvacioj. Serio Internacia
53
2010
435--488
http://fe.math.kobe-u.ac.jp/FE/FullPapers/53-3/53_435.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2761092
For each finite irreducible complex reflection group $G$ in ${\rm GL}(n,{\bf C})$, we construct a system $E_G(z)$ of differential equations on $Z\simeq {\bf P}^{n-1}$ of rank $n$ with the monodromy group $G$, and with the following generating property: If a system $E'(z)$ on $Z$ of rank $n$ has a finite monodromy group and a projective monodromy group which is a subgroup of ${\bf P}(G)$, there is an algebraic transformation $E'(z)=\theta(z)^{1/k} E_G(\sigma(z))$, where $k$ is an integer, $\theta(z)$ a rational function on $Z$, and $\sigma(z)$ a rational map of $Z$ to $Z$. For $n=2,3$, we give explicit forms of $E_G(z)$. Several examples of the above algebraic transformation are also given.
Generating system, Complex reflection group, Hypergeometric function, Schwarz map, Monodromy group.
Primary 33C20.
53-435
2010
Generating Systems for Finite Irreducible Complex Reflection Groups
Yoshishige HARAOKA and Mitsuo KATO
Yoshishige HARAOKA and Mitsuo KATO
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