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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

    • 早田, 孝博 ハヤタ, タカヒロ

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

早田, 孝博

著者別名

ハヤタ, タカヒロ

学位授与大学

神戸大学

取得学位

博士 (理学)

学位授与番号

甲第1588号

学位授与年月日

1996-09-30

注記・抄録

博士論文

目次

  1. Contents / p9 (0005.jp2)
  2. Introduction / p7 (0003.jp2)
  3. Part I. General Results on the Representations of SU(2,2) / p1 (0006.jp2)
  4. 1. The structure of SU(2,2) and its Lie algebra / p2 (0007.jp2)
  5. 1.1. SU(2,2) and its Lie algebra / p2 (0007.jp2)
  6. 1.2. Cuspidal parabolic subgroups of SU(2,2) / p4 (0008.jp2)
  7. 1.3. Iwasawa decomposition of absolute root vectors / p5 (0008.jp2)
  8. 2. Admissible representations of G and their K-types / p6 (0009.jp2)
  9. 2.1. Parametrization of irreducible representations of K / p6 (0009.jp2)
  10. 2.2. Infinitesimal representations of K / p7 (0009.jp2)
  11. 2.3. Contragredient representations of K / p7 (0009.jp2)
  12. 2.4. Adjoint representation of K / p7 (0009.jp2)
  13. 2.5. Principal Pm-series representations / p9 (0010.jp2)
  14. 2.6. Principal Pj-series representations / p10 (0011.jp2)
  15. 2.7. Discrete series representations / p10 (0011.jp2)
  16. 2.8. The multiplicity of K-types / p11 (0011.jp2)
  17. 2.9. K-isotypic components of the principal Pm-series representations / p15 (0013.jp2)
  18. 2.10. An operator between one-dimensional K-types / p17 (0014.jp2)
  19. 2.11. An operator between two-dimensional K-types / p19 (0015.jp2)
  20. 3. Whittaker functions,shift operators and the Casimir operator / p22 (0017.jp2)
  21. 3.1. Whittaker functions / p22 (0017.jp2)
  22. 3.2. Dimension of the space of the Whittaker vectors / p23 (0017.jp2)
  23. 3.3. The Schmid operator / p24 (0018.jp2)
  24. 3.4. Radial part of the Schmid operator / p25 (0018.jp2)
  25. 3.5. Radial part of shift operators / p27 (0019.jp2)
  26. 3.6. Radial part of the Casimir operator / p31 (0021.jp2)
  27. 3.7. Infinitesimal character of principal series representations / p33 (0022.jp2)
  28. Part II. Whittaker Functions of Admissible Representations / p35 (0023.jp2)
  29. 4. Discrete series Whittaker functions / p36 (0024.jp2)
  30. 4.1. Result of Yamashita / p36 (0024.jp2)
  31. 4.2. Radial Am-part of the differential operator Dղ,ɖ / p36 (0024.jp2)
  32. 4.3. Integral expression of discrete series Whittaker functions / p39 (0025.jp2)
  33. 5. Pj-series Whittaker functions / p41 (0026.jp2)
  34. 5.1. Corner K-types of Pj-series representations / p41 (0026.jp2)
  35. 5.2. Differential equations for Whittaker functions / p41 (0026.jp2)
  36. 5.3. Integral expression of Whittaker functions / p44 (0028.jp2)
  37. 6. Pm-series Whittaker functions / p46 (0029.jp2)
  38. 6.1. Differential equations for Whittaker functions / p46 (0029.jp2)
  39. 6.2. Radial part of shift operators(one-dimensional K-type case) / p48 (0030.jp2)
  40. 6.3. Radial part of shift operators(two-dimensional K-type case) / p49 (0030.jp2)
  41. 6.4. Proof of Theorem 6.1 / p50 (0031.jp2)
  42. 6.5. Proof of Theorem 6.2 / p52 (0032.jp2)
  43. Appendix:A. Holonomicity of the System of Differential Equations / p54 (0033.jp2)
  44. A.1. Term order and Gröbner basis / p54 (0033.jp2)
  45. A.2. Characteristic varieties / p55 (0033.jp2)
  46. A.3. Proof of holonomicity / p56 (0034.jp2)
  47. Appendix: B. The structure of Z(gc) / p59 (0035.jp2)
  48. References / p61 (0036.jp2)
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各種コード

  • NII論文ID(NAID)
    500000150574
  • NII著者ID(NRID)
    • 8000001061420
  • DOI(NDL)
  • NDL書誌ID
    • 000000314888
  • データ提供元
    • NDL-OPAC
    • NDLデジタルコレクション
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