Schwarz maps of hypergeometric differential equations with finite monodromy groups

具有有限单向群的超几何微分方程的 Schwarz 图

• 批准号: 12640031
• 负责人: KATO Mituso
• 金额: $ 0.32万
• 依托单位: University of the Ryukyus
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640031/
• 关键词: hypergeometric function; monodromy group; Schwarz map; monodreomy group

Appell's hypergeometric function F_2(a; b, b'; c, c'; x, y) =Σ^^∞__<m,n=0>((a,m+n)(b,m)(b',n))/((c,m)(c',n)(1,m)(1,n))x^my^n, where(a,n) = Γ(a+n)/Γ(a), satisfies a system E_2(a;b,b';c,c') of differential equations on the (x,y)-space X (【similar or equal】P^2).1. I tabulated all the systems of parameters (a;b,b';c,c') into six classes such that each E_2(a;b,b';c,c') has a finite irreducible monodromy group. These monodromy groups have reflection subgroups whose Shephard-Todd numbers are 2,28,30 and 32.2. The system E: = E_2(-1/<12>;1/6;1/<12>;1/3;1/2) has the biggest finite irreducible monodromy group G of order 12・25920. A Schwarz map s_E of E defined by the ratio of four linearly independent solutions of E is a 25920-valued map of X-Sing(E) into P^3, where Sing(E) denotes the singular locus of E. The closure S of the image of s_E turns out to be an irreducible hypersurface of degree 90 on which G acts.

Appell超几何函数F_2(a；b，b‘；c，c’；x，y)=Σ^^∞__&lt；m，n=0&gt；((a，m+n)(b，m)(b‘，n))/((c，m)(c’，n)(1，m)(1，n))x^my^n，其中(a，n)=Γ(a+n)/Γ(A)满足系统E_2(a；b，b‘)；(x，y)-空间X([相似或相等]P^2).我把所有的参数系(a；b，b‘；c，c’)分成六类，使得每个E_2(a；b，b‘；c，c’)都有一个有限不可约单元群。这些单列群有Shephard-Todd数为2、28、30和32.2的反射子群。系统E：=E_2(-1/&lt；12&gt；；1/6；1/&lt；12&gt；；1/3；1/2)有12·25920阶的最大有限不可约单调群G。由E的四个线性无关解之比定义的E的Schwarz映射S_E是X-Sing(E)到P^3的25920值映射，其中Sing(E)表示E的奇异轨迹。S_E像的闭包S是G作用在其上的90次不可约超曲面。

项目成果

M.Kato: "Appell's hypergeometric systems F_2 with finite irreducible monodromy groups"Kyushu J. of Math.. 54. 279-305 (2000)

M.Kato：“具有有限不可约单数群的阿佩尔超几何系统 F_2”Kyushu J. of Math.. 54. 279-305 (2000)

M.Kato: "A simple Pfaffian form representing the hypergeometric differential equation of type (3,6)"Kyushu J. of Math.. 54. 219-224 (2000)

M.Kato：“表示 (3,6) 型超几何微分方程的简单普法夫形式”Kyushu J. of Math.. 54. 219-224 (2000)

M. Kato: "Appell's hypergeometric systems F_2 with finite.irreducible monodromy groups"Kyushu J. of Math. Vol.54. 279-305 (2000)

M. Kato：“Appell 的超几何系统 F_2 与有限不可约单峰群”Kyushu J. of Math。

M. Kato: "A simple Pfaffian form representing the hypergeometric differential equation of type (3,6)"Kyushu J. of Math. Vol.54. 219-224 (2000)

M. Kato：“表示 (3,6) 型超几何微分方程的简单普法夫形式”Kyushu J. of Math。

M.Kato: "A simple Pfaffian form representing the hypergeometric differential equation of type (3,6)"Kyushu J.of Math.. 54. 219-224 (2000)

M.Kato：“表示 (3,6) 型超几何微分方程的简单普法夫形式”Kyushu J.of Math.. 54. 219-224 (2000)