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Richardson elements for classical Lie algebras
- Source :
-
Journal of Algebra . Mar2006, Vol. 297 Issue 1, p168-185. 18p. - Publication Year :
- 2006
-
Abstract
- Abstract: Parabolic subalgebras of semi-simple Lie algebras decompose as where is a Levi factor and the corresponding nilradical. By Richardson''s theorem [R.W. Richardson, Bull. London Math. Soc. 6 (1974) 21–24], there exists an open orbit under the action of the adjoint group P on the nilradical. The elements of this dense orbits are known as Richardson elements. In this paper we describe a normal form for Richardson elements in the classical case. This generalizes a construction for of Brüstle et al. [Algebr. Represent. Theory 2 (1999) 295–312] to the other classical Lie algebra and it extends the authors normal forms of Richardson elements for nice parabolic subalgebras of simple Lie algebras to arbitrary parabolic subalgebras of the classical Lie algebras [K. Baur, Represent. Theory 9 (2005) 30–45]. As applications we obtain a description of the support of Richardson elements and we recover the Bala–Carter label of the orbit of Richardson elements. [Copyright &y& Elsevier]
- Subjects :
- *LIE algebras
*LINEAR algebra
*MATHEMATICAL analysis
*FACTORS (Algebra)
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 297
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 19860616
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2005.03.033