Mendeley出力
＜図書＞
Commensurabilities among lattices in PU(1,n)
| 責任表示 | by Pierre Deligne and G. Daniel Mostow |
|---|---|
| シリーズ | Annals of mathematics studies ; no. 132 |
| データ種別 | 図書 |
| 出版情報 | Princeton, N.J. : Princeton University Press , 1993 |
| 本文言語 | 英語 |
| 大きさ | 183 p. ; 24 cm |
| 概要 | The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensiona... vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometric-like functions by their exponents at the divisors at infinity permits one to prove generalizations in n-variables of the Kummer identities for n-1 involving quadratic and cubic changes of the variable. The first part of this monograph is devoted to a characterization of hypergeometric-like functions, that is, twists of hypergeometric functions in n-variables. These are treated as an (n+1) dimensional vector space of multivalued locally holomorphic functions defined on the space of n+3 tuples of distinct points on the projective line P modulo, the diagonal section of Auto P=m. For n=1, the characterization may be regarded as a generalization of Riemann's classical theorem characterizing hypergeometric functions by their exponents at three singular points. This characterization permits the authors to compare monodromy groups corresponding to different parameters and to prove commensurability modulo inner automorphisms of PU(1,n). The book includes an investigation of elliptic and parabolic monodromy groups, as well as hyperbolic monodromy groups. The former play a role in the proof that a surprising number of lattices in PU(1,2) constructed as the fundamental groups of compact complex surfaces with constant holomorphic curvature are in fact conjugate to projective monodromy groups of hypergeometric functions. The characterization of hypergeometric-like functions by their exponents at the divisors at infinity permits one to prove generalizations in n-variables of the Kummer identities for n-1 involving quadratic and cubic changes of the variable. 続きを見る |
| 電子版へのリンク | https://hdl.handle.net/2324/6822661 |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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理系図3F 数理独自 | DELI/10/1 | 1993 |
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068222195011461 |
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理系図 自動書庫 | 417/D 55/1 | 1993 |
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068582194023988 |
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: pbk | 中央図 3E | 413.5/D 55/58942077 | 1993 |
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068582194020777 |
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書誌詳細
| 一般注記 | Includes bibliographical references (p. [182]-183) |
|---|---|
| 著者標目 | Deligne, Pierre Mostow, George D., 1923- |
| 件 名 | LCSH:Functions, Hypergeometric LCSH:Monodromy groups LCSH:Lattice theory |
| 分 類 | LCC:QA353.H9 DC20:515/.25 NDC8:413.5 |
| 書誌ID | 1001055280 |
| ISBN | 0691033854 |
| NCID | BA20982476 |
| 巻冊次 | ISBN:0691033854 ; PRICE:$49.95 : pbk ; ISBN:0691000964 ; PRICE:$19.95 |
| 登録日 | 2009.09.17 |
| 更新日 | 2009.11.02 |