Crystal bases for quantum classical algebras and Nakajima's monomials

Seok Jin Kang; Jeong Ah Kim; Dong Uy Shin

doi:10.2977/prims/1145475492

Crystal bases for quantum classical algebras and Nakajima's monomials

Seok Jin Kang, Jeong Ah Kim, Dong Uy Shin

Department of Mathematics

Korea Institute for Advanced Study

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

20 Scopus citations

Abstract

Using Nakajima's monomials, we construct a new realization of crystal bases for finite dimensional irreducible modules over quantum classical algebras. We also give an explicit bijection between the monomial realization and the Young tableau realization of crystal bases.

Original language	English
Pages (from-to)	757-791
Number of pages	35
Journal	Publications of the Research Institute for Mathematical Sciences
Volume	40
Issue number	3
DOIs	https://doi.org/10.2977/prims/1145475492
State	Published - Sep 2004

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abstract = "Using Nakajima's monomials, we construct a new realization of crystal bases for finite dimensional irreducible modules over quantum classical algebras. We also give an explicit bijection between the monomial realization and the Young tableau realization of crystal bases.",

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JO - Publications of the Research Institute for Mathematical Sciences

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Crystal bases for quantum classical algebras and Nakajima's monomials

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