A Littlewood-Richardson rule for evaluation representations of .
Leclerc, Bernard (2003)
Séminaire Lotharingien de Combinatoire [electronic only]
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Leclerc, Bernard (2003)
Séminaire Lotharingien de Combinatoire [electronic only]
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Leclerc, Bernard, Thibon, Jean-Yves (1996)
The Electronic Journal of Combinatorics [electronic only]
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Molev, A. I.
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Olivier Mathieu (2000)
Annales de l'institut Fourier
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Let be a reductive Lie algebra and let be a Cartan subalgebra. A -module is called a if and only if , where each weight space is finite dimensional. The main result of the paper is the classification of all simple weight -modules. Further, we show that their characters can be deduced from characters of simple modules in category .
Anthony Joseph, Gail Letzter (1995)
Annales scientifiques de l'École Normale Supérieure
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Yuqun Chen, Yongshan Chen, Chanyan Zhong (2010)
Czechoslovak Mathematical Journal
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We investigate the relationship between the Gröbner-Shirshov bases in free associative algebras, free left modules and “double-free” left modules (that is, free modules over a free algebra). We first give Chibrikov’s Composition-Diamond lemma for modules and then we show that Kang-Lee’s Composition-Diamond lemma follows from it. We give the Gröbner-Shirshov bases for the following modules: the highest weight module over a Lie algebra , the Verma module over a Kac-Moody algebra, the...