Universal Verma modules and the Misra-Miwa Fock space.

Ram, Arun; Tingley, Peter

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A Littlewood-Richardson rule for evaluation representations of $U_{q} ({\hat{𝔰𝔩}}_{n})$ .

Leclerc, Bernard (2003)

Séminaire Lotharingien de Combinatoire [electronic only]

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The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at $q = 0$ .

Leclerc, Bernard, Thibon, Jean-Yves (1996)

The Electronic Journal of Combinatorics [electronic only]

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On certain class of unitarizable representations of the Lie algebra $u (p, q)$

Molev, A. I.

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Classification of irreducible weight modules

Olivier Mathieu (2000)

Annales de l'institut Fourier

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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 $M = \oplus_{λ} M_{λ}$ , 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 $𝒪$ .

Verma module annihilators for quantized enveloping algebras

Anthony Joseph, Gail Letzter (1995)

Annales scientifiques de l'École Normale Supérieure

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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 $s l_{2}$ , the Verma module over a Kac-Moody algebra, the...

Displaying similar documents to “Universal Verma modules and the Misra-Miwa Fock space.”

A Littlewood-Richardson rule for evaluation representations of U q ( 𝔰𝔩 ^ n ) .

The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at q = 0 .

On certain class of unitarizable representations of the Lie algebra u ( p , q )

Classification of irreducible weight modules

Verma module annihilators for quantized enveloping algebras

Composition-diamond lemma for modules

A Littlewood-Richardson rule for evaluation representations of $U_{q} ({\hat{𝔰𝔩}}_{n})$ .

The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at $q = 0$ .

On certain class of unitarizable representations of the Lie algebra $u (p, q)$