Monomial realization of the crystals over Uq(A∞) and the quantum monster algebra

Jeong Ah Kim; Dong Uy Shin

doi:10.1080/00927870902828652

Monomial realization of the crystals over U_q(A_∞) and the quantum monster algebra

Jeong Ah Kim, Dong Uy Shin

Department of Mathematics

Hanyang University

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

2 Scopus citations

Abstract

We give new realizations of the crystal bases of the Verma modules and the irreducible highest weight modules over the quantum generalized Kac-Moody algebra U_q(A_∞) and the quantum Monster algebra using Nakajima monomials. Moreover, another realization of the crystals B(∞) and B(λ) over U_q(A_∞) using triangular matrices and tableaux are given.

Original language	English
Pages (from-to)	890-907
Number of pages	18
Journal	Communications in Algebra
Volume	38
Issue number	3
DOIs	https://doi.org/10.1080/00927870902828652
State	Published - Mar 2010

Keywords

Crystals
Nakajima monomials

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10.1080/00927870902828652

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title = "Monomial realization of the crystals over Uq(A∞) and the quantum monster algebra",

abstract = "We give new realizations of the crystal bases of the Verma modules and the irreducible highest weight modules over the quantum generalized Kac-Moody algebra Uq(A∞) and the quantum Monster algebra using Nakajima monomials. Moreover, another realization of the crystals B(∞) and B(λ) over Uq(A∞) using triangular matrices and tableaux are given.",

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AB - We give new realizations of the crystal bases of the Verma modules and the irreducible highest weight modules over the quantum generalized Kac-Moody algebra Uq(A∞) and the quantum Monster algebra using Nakajima monomials. Moreover, another realization of the crystals B(∞) and B(λ) over Uq(A∞) using triangular matrices and tableaux are given.

KW - Crystals

KW - Nakajima monomials

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DO - 10.1080/00927870902828652

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SN - 0092-7872

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EP - 907

JO - Communications in Algebra

JF - Communications in Algebra

IS - 3

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Monomial realization of the crystals over U_q(A_∞) and the quantum monster algebra

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Keywords

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