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李群的表示Representations of Lie Groups |
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| 课程网址: | https://ocw.mit.edu/courses/18-757-representations-of-lie-groups-... |
| 主讲教师: | Prof. Pavel Etingof |
| 开课单位: | 麻省理工学院 |
| 开课时间: | 2023-01-01 |
| 课程语种: | 英语 |
| 中文简介: |  |
| 课程简介: | The goal of this course is to give an introduction to the representation theory of compact and non-compact Lie groups. It will rely on some material from 18.745 Lie Groups and Lie Algebras I and 18.755 Lie Groups and Lie Algebras II, but full familiarity with this material is not required. Topics include continuous representations; algebras of measures on a Lie group; K-finite, smooth, and analytic vectors; admissible representations; unitary representations; the Harish-Chandra admissibility and analyticity theorems; (g,K)-modules; infinitesimal equivalence and realizations; Harish-Chandra’s globalization theorem; representations of SL(2,R), the Chevalley restriction theorem; the Chevalley-Shepard-Todd theorem; Kostant’s theorem; Harish-Chandra isomorphism; Bernstein-Gelfand-Gelfand category O; projective functors; classification of irreducible Harish-Chandra bimodules; the nilpotent cone; the Duflo-Joseph theorem; Duflo’s primitive ideal theorem; the Borel-Weil theorem; Springer resolution; Beilinson-Bernstein localization; D-modules; and classification of representations of a semisimple real group in terms of the orbits of the complexified maximal compact subgroup on the flag variety. |
| 关 键 词: | 紧实非紧李群; 表示理论; 群上测度 |
| 课程来源: | 麻省理工学院公开课 |
| 数据采集: | 2024-12-28：chenjy |
| 最后编审: | 2024-12-28：chenjy |
| 阅读次数: | 253 |