Highest weight modules for semisimple Lie algebras

1980 ◽  
pp. 72-103 ◽  
Author(s):  
James E. Humphreys
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

Categories of nonstandard highest weight modules for affine Lie algebras

1996 ◽  
Vol 221 (1) ◽  
pp. 193-209 ◽  
Author(s):  
B. Cox ◽  
V. Futorny ◽  
D. Melville
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

scholarly journals Classification of irreducible integrable highest weight modules for current Kac–Moody algebras

2016 ◽  
Vol 16 (07) ◽  
pp. 1750123 ◽  
Author(s):  
S. Eswara Rao ◽  
Punita Batra
Keyword(s):  
Lie Algebras ◽  
Direct Sums ◽  
Highest Weight ◽  
Finite Dimensional ◽  
Highest Weight Modules ◽  
Weight Modules

This paper classifies irreducible, integrable highest weight modules for “current Kac–Moody Algebras” with finite-dimensional weight spaces. We prove that these modules turn out to be modules of appropriate direct sums of finitely many copies of Kac–Moody Lie algebras.

A Reduction Theorem for Highest Weight Modules over Toroidal Lie Algebras

2004 ◽  
Vol 250 (1) ◽  
pp. 47-63 ◽  
Author(s):  
Ivan Dimitrov ◽  
Vyacheslav Futorny ◽  
Ivan Penkov
Keyword(s):  
Lie Algebras ◽  
Reduction Theorem ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules

Categories of nonstandard highest weight modules for affine Lie algebras

1996 ◽  
Vol 221 (2) ◽  
pp. 193-209 ◽  
Author(s):  
B. Cox ◽  
V. Futorny ◽  
D. Melville
Keyword(s):  
Lie Algebras ◽  
Affine Lie Algebras ◽  
Highest Weight ◽  
Highest Weight Modules ◽  
Weight Modules
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