NICE PARABOLIC SUBALGEBRAS OF REDUCTIVE LIE ALGEBRAS
作者： Karin Baur , Nolan Wallach
DOI: 10.1090/S1088-4165-05-00262-1
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摘要: This paper gives a classification of parabolic subalgebras simple Lie algebras over C that are complexifications real forms for which Lynch’s vanishing theorem generalized Whittaker modules is non-vacuous. The also describes normal the admissible characters in sense Lynch (at least quasi-split cases) and analyzes important special case when defined by an even embedded TDS (three dimensional algebra).
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sci-hub.st 参考文章(11)
Thomas Brüstle, Lutz Hille, Claus Michael Ringel, Gerhard Röhrle, None, The Δ-Filtered Modules Without Self-Extensions for the Auslander Algebra of k[ T ]/〈 T n 〉 Algebras and Representation Theory. ,vol. 2, pp. 295- 312 ,(1999) , 10.1023/A:1009999006899
M. Geck, Finite groups of Lie type ,(1985)
Nolan R. Wallach, Roe Goodman, Representations and invariants of the classical groups ,(1998)
Thomas Emile Lynch, Generalized Whittaker vectors and representation theory. Massachusetts Institute of Technology. ,(1979)
Roger W. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters ,(1993)
V. G. Kac, A. G. Elashvili, Good Gradings of Simple Lie Algebras arXiv: Mathematical Physics. ,(2003)
D. S. Johnston, R. W. Richardson, Conjugacy Classes in Parabolic Subgroups of Semisimple Algebraic Groups, II Bulletin of the London Mathematical Society. ,vol. 9, pp. 245- 250 ,(1977) , 10.1112/BLMS/9.3.245
Simon Goodwin, Gerhard Röhrle, Prehomogeneous spaces for parabolic group actions in classical groups Journal of Algebra. ,vol. 276, pp. 383- 398 ,(2004) , 10.1016/J.JALGEBRA.2003.11.005
William M. McGovern, David H. Collingwood, Nilpotent orbits in semisimple Lie algebras Van Nostrand Reinhold. ,(1993)
Bertram Kostant, On Whittaker vectors and representation theory Inventiones Mathematicae. ,vol. 48, pp. 101- 184 ,(1978) , 10.1007/BF01390249