For each finite irreducible complex reflection group
G in GL(
n,
C), we construct a system
EG(
z) of differential equations on
Z $\simeq$
Pn-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
P(
G), there is an algebraic transformation
E′(
z) = θ(
z)
1/kEG(σ(
z)),
where
k is an integer, θ(
z) a rational function on
Z, and σ(
z) a rational map of
Z to
Z. For
n = 2, 3, we give explicit forms of
EG(
z). Several examples of the above algebraic transformation are also given.
抄録全体を表示