Insertion scheme for the classical Lie algebras

Jeong Ah Kim; Dong Uy Shin

doi:10.1081/AGB-120039283

Insertion scheme for the classical Lie algebras

Jeong Ah Kim, Dong Uy Shin

Department of Mathematics

Korea Institute for Advanced Study

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we give an insertion scheme for the tableaux of Kashiwara-Nakashima realizing the crystal bases of the irreducible highest weight modules over the classical Lie algebras. It gives an explicit combinatorial description of the decomposition of the tensor product V(λ) ⊗ V(μ) into irreducible modules.

Original language	English
Pages (from-to)	3139-3167
Number of pages	29
Journal	Communications in Algebra
Volume	32
Issue number	8
DOIs	https://doi.org/10.1081/AGB-120039283
State	Published - 2004

Keywords

Classical Lie algebra
Crystal base
Insertion scheme

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10.1081/AGB-120039283

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title = "Insertion scheme for the classical Lie algebras",

abstract = "In this paper, we give an insertion scheme for the tableaux of Kashiwara-Nakashima realizing the crystal bases of the irreducible highest weight modules over the classical Lie algebras. It gives an explicit combinatorial description of the decomposition of the tensor product V(λ) ⊗ V(μ) into irreducible modules.",

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AU - Shin, Dong Uy

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AB - In this paper, we give an insertion scheme for the tableaux of Kashiwara-Nakashima realizing the crystal bases of the irreducible highest weight modules over the classical Lie algebras. It gives an explicit combinatorial description of the decomposition of the tensor product V(λ) ⊗ V(μ) into irreducible modules.

KW - Classical Lie algebra

KW - Crystal base

KW - Insertion scheme

UR - https://www.scopus.com/pages/publications/8344241626

U2 - 10.1081/AGB-120039283

DO - 10.1081/AGB-120039283

M3 - Article

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SN - 0092-7872

VL - 32

SP - 3139

EP - 3167

JO - Communications in Algebra

JF - Communications in Algebra

IS - 8

ER -

Insertion scheme for the classical Lie algebras

Abstract

Keywords

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