scholarly journals Levi components of parabolic subalgebras of finitary Lie algebras

2011 ◽  
pp. 129-149 ◽  
Author(s):  
Elizabeth Dan-Cohen ◽  
Ivan Penkov
Keyword(s):  
Lie Algebras ◽  
Parabolic Subalgebras

Affine Lie Algebra Modules and Complete Lie Algebras

2006 ◽  
Vol 13 (03) ◽  
pp. 481-486
Author(s):  
Yongcun Gao ◽  
Daoji Meng
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Infinite Dimensional ◽  
Affine Lie Algebra ◽  
Parabolic Subalgebras ◽  
Integrable Modules

In this paper, we first construct some new infinite dimensional Lie algebras by using the integrable modules of affine Lie algebras. Then we prove that these new Lie algebras are complete. We also prove that the generalized Borel subalgebras and the generalized parabolic subalgebras of these Lie algebras are complete.

The branching problem for generalized Verma modules, with application to the pair (so(7), LieG2)

2014 ◽  
Vol 13 (07) ◽  
pp. 1450034
Author(s):  
Todor Milev ◽  
Petr Somberg
Keyword(s):  
Large Class ◽  
Lie Algebras ◽  
Verma Modules ◽  
Singular Vectors ◽  
Weakly Compatible ◽  
Parabolic Subalgebras ◽  
Generalized Verma Modules ◽  
Branching Problem ◽  
Character Formulas

We consider the branching problem for generalized Verma modules Mλ(𝔤, 𝔭) applied to couples of reductive Lie algebras [Formula: see text]. Our analysis of the problem is based on projecting character formulas to quantify the branching, and on the action of the center of [Formula: see text] to construct explicitly singular vectors realizing the [Formula: see text]-top level of the branching. We compute explicitly the top part of the branching for the pair [Formula: see text] for both strongly and weakly compatible with i( Lie G2) parabolic subalgebras and a large class of inducing representations.

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