Nakajima monomials, Young walls and Kashiwara embedding for U-q(A(n)((1)))

Title
Nakajima monomials, Young walls and Kashiwara embedding for U-q(A(n)((1)))
Author
신동의
Keywords
Nakajima monomials; Young walls; Kashiwara embeddings; Crystal bases
Issue Date
2011-03
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
JOURNAL OF ALGEBRA, v. 330, NO 1, Page. 234-250
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. (C) 2010 Elsevier Inc. All rights reserved.
URI
https://www.sciencedirect.com/science/article/pii/S0021869310005983http://hdl.handle.net/20.500.11754/66436
DOI
10.1016/j.jalgebra.2010.11.010
Appears in Collections:
COLLEGE OF EDUCATION[S](사범대학) > MATHEMATICS EDUCATION(수학교육과) > Articles
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