A Littlewood-Richardson rule for evaluation representations of .
Leclerc, Bernard (2003)
Séminaire Lotharingien de Combinatoire [electronic only]
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Displaying similar documents to “Combinatorial bases of modules for affine Lie algebra B 2(1)”
A Littlewood-Richardson rule for evaluation representations of .
The 3-state Potts model and Rogers-Ramanujan series
Alex Feingold, Antun Milas (2013)
Open Mathematics
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We explain the appearance of Rogers-Ramanujan series inside the tensor product of two basic A 2(2) -modules, previously discovered by the first author in [Feingold A.J., Some applications of vertex operators to Kac-Moody algebras, In: Vertex Operators in Mathematics and Physics, Berkeley, November 10–17, 1983, Math. Sci. Res. Inst. Publ., 3, Springer, New York, 1985, 185–206]. The key new ingredients are (5,6)Virasoro minimal models and twisted modules for the Zamolodchikov W 3-algebra. ...
The combinatorics of the Garsia-Haiman modules for hook shapes.
Adin, Ron M., Remmel, Jeffrey B., Roichman, Yuval (2008)
The Electronic Journal of Combinatorics [electronic only]
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Constructing homomorphisms between Verma modules.
de Graaf, Willem A. (2005)
Journal of Lie Theory
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Generalized Verma module homomorphisms in singular character
Peter Franek (2006)
Archivum Mathematicum
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In this paper we study invariant differential operators on manifolds with a given parabolic structure. The model for the parabolic geometry is the quotient of the orthogonal group by a maximal parabolic subgroup corresponding to crossing of the -th simple root of the Dynkin diagram. In particular, invariant differential operators discussed in the paper correspond (in a flat model) to the Dirac operator in several variables.
Composition-diamond lemma for modules
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...
Quasitriangular Hopf group algebras and braided monoidal categories
Shiyin Zhao, Jing Wang, Hui-Xiang Chen (2014)
Czechoslovak Mathematical Journal
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Let be a group, and be a semi-Hopf -algebra. We first show that the category of left -modules over is a monoidal category with a suitably defined tensor product and each element in induces a strict monoidal functor from to itself. Then we introduce the concept of quasitriangular semi-Hopf -algebra, and show that a semi-Hopf -algebra is quasitriangular if and only if the category is a braided monoidal category and is a strict braided monoidal functor for any...