论文信息 - NICE PARABOLIC SUBALGEBRAS OF REDUCTIVE LIE ALGEBRAS

NICE PARABOLIC SUBALGEBRAS OF REDUCTIVE LIE ALGEBRAS

This paper gives a classification of parabolic subalgebras of simple Lie algebras over C that are complexifications of parabolic subalgebras of real forms for which Lynch’s vanishing theorem for generalized Whittaker modules is non-vacuous. The paper also describes normal forms for the admissible characters in the sense of Lynch (at least in the quasi-split cases) and analyzes the important special case when the parabolic is defined by an even embedded TDS (three dimensional simple Lie algebra).

Karin Baur | Nolan Wallach | N. Wallach | K. Baur

[1] Good Gradings of Simple Lie Algebras , 2003, math-ph/0312030.

[2] William M. McGovern,et al. Nilpotent orbits in semisimple Lie algebras , 1993 .

[3] R. Goodman,et al. Representations and Invariants of the Classical Groups , 1998 .

[4] Roger W. Carter,et al. Finite groups of Lie type: Conjugacy classes and complex characters , 1985 .

[5] Meinolf Geck,et al. Finite groups of Lie type , 1985 .

[6] G. Andrews. The Theory of Partitions: Frontmatter , 1976 .

[7] R. Richardson,et al. Conjugacy Classes in Parabolic Subgroups of Semisimple Algebraic Groups, II , 1974 .

[8] B. Hilemàn. Van nostrand reinhold. , 1983, Environmental science & technology.

[9] B. Kostant. On Whittaker vectors and representation theory , 1978 .

[10] C. Ringel,et al. The Δ-Filtered Modules Without Self-Extensions for the Auslander Algebra of k[T]/〈Tn〉 , 1999 .

[11] A. Elashvili. Classification of Good Gradings of Simple Lie Algebras , 2005 .

[12] A NORMAL FORM FOR ADMISSIBLE CHARACTERS IN THE SENSE OF LYNCH , 2004, math/0410325.

[13] Simon M. Goodwin,et al. Prehomogeneous spaces for parabolic group actions in classical groups , 2004 .

[14] Thomas Lynch. Generalized Whittaker vectors and representation theory. , 1979 .

[15] N. Wallach. Holomorphic continuation of generalized Jacquet integrals for degenerate principal series , 2006 .