Complexity of Lie algebra representations and nilpotent elements of the stabilizers of linear forms

1998 ◽  
Vol 228 (2) ◽  
pp. 255-282 ◽  
Author(s):  
Alexander Premet
Keyword(s):  
Lie Algebra ◽  
Linear Forms ◽  
Nilpotent Elements ◽  
Lie Algebra Representations

Regge lattice and Lie‐algebra representations

1974 ◽  
Vol 15 (6) ◽  
pp. 857-860 ◽  
Author(s):  
Moshé Flato ◽  
Håkan Snellman
Keyword(s):  
Lie Algebra ◽  
Lie Algebra Representations

Classes of unipotent elements in simple algebraic groups. I

1976 ◽  
Vol 79 (3) ◽  
pp. 401-425 ◽  
Author(s):  
P. Bala ◽  
R. W. Carter
Keyword(s):  
Algebraic Group ◽  
Lie Algebra ◽  
Algebraic Groups ◽  
Adjoint Action ◽  
Conjugacy Classes ◽  
Closed Field ◽  
Algebraically Closed Field ◽  
Nilpotent Elements

LetGbe a simple adjoint algebraic group over an algebraically closed fieldK. We are concerned to describe the conjugacy classes of unipotent elements ofG. Goperates on its Lie algebra g by means of the adjoint action and we may consider classes of nilpotent elements of g under this action. It has been shown by Springer (11) that there is a bijection between the unipotent elements ofGand the nilpotent elements ofgwhich preserves theG-action, provided that the characteristic ofKis either 0 or a ‘good prime’ forG. Thus we may concentrate on the problem of classifying the nilpotent elements of g under the adjointG-action.

Induction, deformation, and specialization of Lie algebra representations

1991 ◽  
Vol 290 (1) ◽  
pp. 473-489 ◽  
Author(s):  
E. M. Friedlander ◽  
B. J. Parshall
Keyword(s):  
Lie Algebra ◽  
Lie Algebra Representations
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