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The Langlands Classification and Irreducible Characters for Real Reductive Groups 1992nd ed.(Progress in Mathematics Vol.104) H

Adams, J., Barbasch, D., Vogan, D.A. 　著

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発行年月	1992年05月
出版社／提供元	Birkhauser Boston
出版国	アメリカ合衆国
言語	英語
媒体	冊子
装丁	hardcover
ページ数／巻数	XII, 320 p.
ジャンル	洋書／理工学／数学／代数学
ISBN	9780817636340
商品コード	0209210638
本の性格	学術書
商品URL	https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=0209210638

内容

IIunit(G(R)) :::> IItemp(G(R)) (1. 1) to be the set ofequivalence classes ofirreducible admissible (respectively unitary or tempered) representations of G(R). Now define (G(R)) :::> temp(G(R)) (1. 2) to be the set ofLanglands parameters for irreducible admissible (respec tively tempered) representations of G(R) (see [34], [10], [1]' Chapter 5, and Definition 22. 3). To each ¢ E (G(R)), Langlands attaches a finite set II C II(G(R)), called an L-packet of representations. The L-packets II partition II(G(R)). If ¢ E temp(G(R)), then the representations in II are all tempered, and in this way one gets also a partition of II (G(R)). temp Now the classification of the unitary representations of G(IR) is one of the most interesting unsolved problems in harmonic analysis.

1. Introduction.- 2. Structure theory: real forms.- 3. Structure theory: extended groups and Whittaker models.- 4. Structure theory: L-groups.- 5. Langlands parameters and L-homomorphisms.- 6. Geometric parameters.- 7. Complete geometric parameters and perverse sheaves.- 8. Perverse sheaves on the geometric parameter space.- 9. The Langlands classification for tori.- 10. Covering groups and projective representations.- 11. The Langlands classification without L-groups.- 12. Langlands parameters and Cartan subgroups.- 13. Pairings between Cartan subgroups and the proof of Theorem 10.4.- 14. Proof of Propositions 13.6 and 13.8.- 15. Multiplicity formulas for representations.- 16. The translation principle, the Kazhdan-Lusztig algorithm, and Theorem 1.24.- 17. Proof of Theorems 16.22 and 16.24.- 18. Strongly stable characters and Theorem 1.29.- 19. Characteristic cycles, micro-packets, and Corollary 1.32.- 20. Characteristic cycles and Harish-Chandra modules.- 21. The classification theorem and Harish-Chandra modules for the dual group.- 22. Arthur parameters.- 23. Local geometry of constructible sheaves.- 24. Microlocal geometry of perverse sheaves.- 25. A fixed point formula.- 26. Endoscopic lifting.- 27. Special unipotent representations.- References.

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