Nakajima monomials and crystals for special linear Lie algebras

2005/06/08 by Hyeonmi Lee, Lee, Hyeonmi
Mathematics · Physics and Astronomy · #17B37 #81R50 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37 #msc:81R50

paper · pdf · doi:10.48550/arxiv.math/0506147

20 pages

openalex publication_date 2005/06/08 · arxiv created 2006/11/21 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present explicit descriptions of the crystals B(∞) and B(λ) over special linear Lie algebras in the language of extended Nakajima monomials. There is a natural correspondence between the monomial description and Young tableau realization, which is another realization of crystals B(∞) and B(λ).

Related

• Crystal \Bla in B(∞) for G₂ type Lie Algebra
• Monomial Relization of Crystal Bases for Special Linear Lie Algebras
• Compression of Nakajima monomials in type A and C
• Crystal Bases and Young Tableaux
• Description of B(∞) through Kashiwara Embedding for E₆ and E₇ Lie Algebra Types