Displaying similar documents to “A Littlewood-Richardson rule for evaluation representations of U q ( 𝔰𝔩 ^ n ) .”

The 3-state Potts model and Rogers-Ramanujan series

Alex Feingold, Antun Milas (2013)

Open Mathematics

Similarity:

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. ...

Composition-diamond lemma for modules

Yuqun Chen, Yongshan Chen, Chanyan Zhong (2010)

Czechoslovak Mathematical Journal

Similarity:

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 s l 2 , the Verma module over a Kac-Moody algebra, the...

Classification of irreducible weight modules

Olivier Mathieu (2000)

Annales de l'institut Fourier

Similarity:

Let 𝔤 be a reductive Lie algebra and let 𝔥 be a Cartan subalgebra. A 𝔤 -module M is called a if and only if M = λ M λ , where each weight space M λ is finite dimensional. The main result of the paper is the classification of all simple weight 𝔤 -modules. Further, we show that their characters can be deduced from characters of simple modules in category 𝒪 .

Combinatorial bases of modules for affine Lie algebra B 2(1)

Mirko Primc (2013)

Open Mathematics

Similarity:

We construct bases of standard (i.e. integrable highest weight) modules L(Λ) for affine Lie algebra of type B 2(1) consisting of semi-infinite monomials. The main technical ingredient is a construction of monomial bases for Feigin-Stoyanovsky type subspaces W(Λ) of L(Λ) by using simple currents and intertwining operators in vertex operator algebra theory. By coincidence W(kΛ0) for B 2(1) and the integrable highest weight module L(kΛ0) for A 1(1) have the same parametrization of combinatorial...