Whittaker functions of admissible representations on SU(2,2) SU(2,2)上の許容表現に付随するウィッタカー関数
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著者
書誌事項
- タイトル
-
Whittaker functions of admissible representations on SU(2,2)
- タイトル別名
-
SU(2,2)上の許容表現に付随するウィッタカー関数
- 著者名
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早田, 孝博
- 著者別名
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ハヤタ, タカヒロ
- 学位授与大学
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神戸大学
- 取得学位
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博士 (理学)
- 学位授与番号
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甲第1588号
- 学位授与年月日
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1996-09-30
注記・抄録
博士論文
目次
- Contents / p9 (0005.jp2)
- Introduction / p7 (0003.jp2)
- Part I. General Results on the Representations of SU(2,2) / p1 (0006.jp2)
- 1. The structure of SU(2,2) and its Lie algebra / p2 (0007.jp2)
- 1.1. SU(2,2) and its Lie algebra / p2 (0007.jp2)
- 1.2. Cuspidal parabolic subgroups of SU(2,2) / p4 (0008.jp2)
- 1.3. Iwasawa decomposition of absolute root vectors / p5 (0008.jp2)
- 2. Admissible representations of G and their K-types / p6 (0009.jp2)
- 2.1. Parametrization of irreducible representations of K / p6 (0009.jp2)
- 2.2. Infinitesimal representations of K / p7 (0009.jp2)
- 2.3. Contragredient representations of K / p7 (0009.jp2)
- 2.4. Adjoint representation of K / p7 (0009.jp2)
- 2.5. Principal Pm-series representations / p9 (0010.jp2)
- 2.6. Principal Pj-series representations / p10 (0011.jp2)
- 2.7. Discrete series representations / p10 (0011.jp2)
- 2.8. The multiplicity of K-types / p11 (0011.jp2)
- 2.9. K-isotypic components of the principal Pm-series representations / p15 (0013.jp2)
- 2.10. An operator between one-dimensional K-types / p17 (0014.jp2)
- 2.11. An operator between two-dimensional K-types / p19 (0015.jp2)
- 3. Whittaker functions,shift operators and the Casimir operator / p22 (0017.jp2)
- 3.1. Whittaker functions / p22 (0017.jp2)
- 3.2. Dimension of the space of the Whittaker vectors / p23 (0017.jp2)
- 3.3. The Schmid operator / p24 (0018.jp2)
- 3.4. Radial part of the Schmid operator / p25 (0018.jp2)
- 3.5. Radial part of shift operators / p27 (0019.jp2)
- 3.6. Radial part of the Casimir operator / p31 (0021.jp2)
- 3.7. Infinitesimal character of principal series representations / p33 (0022.jp2)
- Part II. Whittaker Functions of Admissible Representations / p35 (0023.jp2)
- 4. Discrete series Whittaker functions / p36 (0024.jp2)
- 4.1. Result of Yamashita / p36 (0024.jp2)
- 4.2. Radial Am-part of the differential operator Dղ,ɖ / p36 (0024.jp2)
- 4.3. Integral expression of discrete series Whittaker functions / p39 (0025.jp2)
- 5. Pj-series Whittaker functions / p41 (0026.jp2)
- 5.1. Corner K-types of Pj-series representations / p41 (0026.jp2)
- 5.2. Differential equations for Whittaker functions / p41 (0026.jp2)
- 5.3. Integral expression of Whittaker functions / p44 (0028.jp2)
- 6. Pm-series Whittaker functions / p46 (0029.jp2)
- 6.1. Differential equations for Whittaker functions / p46 (0029.jp2)
- 6.2. Radial part of shift operators(one-dimensional K-type case) / p48 (0030.jp2)
- 6.3. Radial part of shift operators(two-dimensional K-type case) / p49 (0030.jp2)
- 6.4. Proof of Theorem 6.1 / p50 (0031.jp2)
- 6.5. Proof of Theorem 6.2 / p52 (0032.jp2)
- Appendix:A. Holonomicity of the System of Differential Equations / p54 (0033.jp2)
- A.1. Term order and Gröbner basis / p54 (0033.jp2)
- A.2. Characteristic varieties / p55 (0033.jp2)
- A.3. Proof of holonomicity / p56 (0034.jp2)
- Appendix: B. The structure of Z(gc) / p59 (0035.jp2)
- References / p61 (0036.jp2)