Properties of linear representations with a highest weight for the semisimple Lie algebras

1975 ◽  
Vol 16 (9) ◽  
pp. 1816-1832 ◽  
Author(s):  
B. Gruber ◽  
A. U. Klimyk
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras ◽  
Highest Weight ◽  
Linear Representations

scholarly journals A generalization of the alcove model and its applications

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Cristian Lenart ◽  
Arthur Lubovsky
Keyword(s):  
Lie Algebras ◽  
Energy Function ◽  
Tensor Products ◽  
Present Evidence ◽  
Semisimple Lie Algebras ◽  
Highest Weight ◽  
International Audience ◽  
Alcove Model

International audience The alcove model of the first author and Postnikov describes highest weight crystals of semisimple Lie algebras. We present a generalization, called the quantum alcove model, and conjecture that it uniformly describes tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types. We prove the conjecture in types $A$ and $C$. We also present evidence for the fact that a related statistic computes the energy function. Le modèle des alcôves du premier auteur et Postnikov décrit les cristaux de plus haut poids des algèbres de Lie semi-simples. Nous présentons une généralisation, appelée le modèle des alcôves quantique, et nous conjecturons qu’il décrit dans une manière uniforme les produits tensoriels des cristaux de Kirillov-Reshetikhin de type colonne, pour toutes les types affines symétriques. Nous prouvons la conjecture dans les types $A$ et $C$. Nous fournissons aussi des preuves qu’une statistique associée donne la fonction d’énergie.

Linear Representations of Semisimple Lie Algebras

1987 ◽  
pp. 56-65
Author(s):  
Jean-Pierre Serre
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras ◽  
Linear Representations

Properties of Linear Representations of Semisimple Lie Algebras

1973 ◽  
Vol 25 (2) ◽  
pp. 269-286 ◽  
Author(s):  
Bruno Gruber
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras ◽  
Linear Representations

scholarly journals Normal forms of nilpotent elements in semisimple Lie algebras

2021 ◽  
Author(s):  
Mamuka Jibladze ◽  
Victor G. Kac
Keyword(s):  
Lie Algebras ◽  
Normal Forms ◽  
Semisimple Lie Algebras ◽  
Nilpotent Elements

scholarly journals Corrigendum to “Sheets and topology of primitive spectra for semisimple Lie algebras”

2003 ◽  
Vol 259 (1) ◽  
pp. 310-311 ◽  
Author(s):  
Walter Borho ◽  
Anthony Joseph
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras ◽  
And Topology

Semisimple Lie Algebras of Operators

2001 ◽  
pp. 181-202
Author(s):  
Daniel Beltiţă ◽  
Mihai Şabac
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras

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

Semisimple Lie Algebras

2020 ◽  
pp. 71-134
Author(s):  
Morikuni Goto ◽  
Frank D. Grosshans
Keyword(s):  
Lie Algebras ◽  
Semisimple Lie Algebras
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