Nakajima monomials, Young walls and Kashiwara embedding for U-q(A(n)((1)))open access
- Authors
- Kim, Jeong-Ah; Shin, Dong-Uy
- Issue Date
- Mar-2011
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Nakajima monomials; Young walls; Kashiwara embeddings; Crystal bases
- Citation
- JOURNAL OF ALGEBRA, v.330, no.1, pp.234 - 250
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF ALGEBRA
- Volume
- 330
- Number
- 1
- Start Page
- 234
- End Page
- 250
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/168944
- DOI
- 10.1016/j.jalgebra.2010.11.010
- ISSN
- 0021-8693
- Abstract
- In this paper, we realize the crystal basis B(A) of the irreducible highest weight module V(A) of level 1 for U(A) using Nakajima monomials satisfying some conditions. Also, from this monomial realization, we obtain the image of Kashiwara embedding Psi(lambda)(l) : B(lambda) -> Z(infinity) circle times R-lambda, where l is some infinite sequence from the index set of simple roots. Finally, we give a U-q(A(n)((1)))-crystal isomorphism between Young wall realization and monomial realization, and so we can understand the image of Kashiwara embedding Psi(lambda)(l) : B(lambda) -> Z(infinity) circle times R-lambda using the combinatorics of Young walls.
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