Integrable highest weight modules over affine Lie algebras. Application to η-function identities

1983 ◽  
pp. 150-164
Author(s):  
Victor G. Kac
Keyword(s):  
Lie Algebras ◽  
Affine 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

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

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.

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