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| 概要 |
Assume the system of differential equations E_4(a, b, c, c'; X, Y ) satisfied by Appell's hypergeometric function F_4(a, b, c, c'; X, Y ) has a finite irreducible monodromy group M_4(a, b, c, c'). The... monodromy matrix Γ_<3∗> derived from a loop Γ_3 surrounding once the irreducible component C = {(X, Y) | (X − Y)^2 − 2(X + Y) + 1 = 0} of the singular locus of E_4 is a complex reflection. The minimal normal subgroup N_C of M_4 containing Γ_<3∗> is, by definition, a finite complex reflection group of rank four. Let P(G) be the projective monodromy group of the Gauss hypergeometric differential equation _2E_1(a, b, c). It is known that N_C is reducible if ε := c + c' - a - b - 1 ∉ Z or if ε ∈ Z and P(G) is a dihedral group. We prove that, if ε ∈ Z, then N_C is the (irreducible) Coxeter group W(D_4), W(F_4)and W(H_4) according as P(G) is the tetrahedral, octahedral and icosahedral group, respectively.続きを見る
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Mendeley出力
