Monodromy of the Hypergeometric Differential Equation of Type (3, 6) Iii
نویسندگان
چکیده
For the hypergeometric system E(3, 6;α) of type (3, 6), two special cases α ≡ 1/2 and α ≡ 1/6 are studied in [MSY] and [MSTY2], respectively. The monodromy group of the former is an arithmetic group acting on a symmetric domain, and that of the latter is the unitary reflection group ST34. In this paper, we find a relation between these two groups.
منابع مشابه
Halphen's Transform and Middle Convolution 1
Of special interest are those Lamé equations with finite monodromy group, having therefore algebraic solutions, studied by Baldassarri, Beukers and van der Waall, Chudnovsky and Chudnovsky, Dwork and many others (cf. [2], [4], [8] just to mention some papers). Lamé equations also occur in the context of Grothendieck’s p-curvature conjecture (cf. [8, p. 15]). This conjecture says that if the p-c...
متن کاملTransformations of algebraic Gauss hypergeometric functions
A celebrated theorem of Klein implies that any hypergeometric differential equation with algebraic solutions is a pull-back of one of the few standard hypergeometric equations with algebraic solutions. The most interesting cases are hypergeometric equations with tetrahedral, octahedral or icosahedral monodromy groups. We give an algorithm for computing Klein’s pull-back coverings in these cases...
متن کاملOn Generalized Hypergeometric Equations and Mirror Maps
This paper deals with generalized hypergeometric differential equations of order n ≥ 3 having maximal unipotent monodromy at 0. We show that, among these equations, those leading to mirror maps with integral Taylor coefficients at 0 (up to simple rescaling) have special parameters, namely R-partitioned parameters. This result yields the classification of all generalized hypergeometric different...
متن کاملThe Hyperbolic Schwarz Map for the Hypergeometric Differential Equation
The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the singularities of this map, and visual...
متن کاملHyperbolic Schwarz Map for the Hypergeometric Differential Equation
The Schwarz map of the hypergeometric differential equation is studied since the beginning of the last century. Its target is the complex projective line, the 2-sphere. This paper introduces the hyperbolic Schwarz map, whose target is the hyperbolic 3-space. This map can be considered to be a lifting to the 3-space of the Schwarz map. This paper studies the singularities of this map, and visual...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2010