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Zigzag strip bundles and crystalsopen access
- Authors
- Kim, Jeong-Ah; Shin, Dong-Uy
- Issue Date
- Jul-2013
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Zigzag strip bundles; Nakajima monomials; Kashiwara embeddings; Crystals
- Citation
- JOURNAL OF COMBINATORIAL THEORY SERIES A, v.120, no.5, pp.1087 - 1115
- Indexed
- SCIE
SCOPUS
- Journal Title
- JOURNAL OF COMBINATORIAL THEORY SERIES A
- Volume
- 120
- Number
- 5
- Start Page
- 1087
- End Page
- 1115
- ISSN
- 0097-3165
- Abstract
- We introduce new combinatorial models, called zigzag strip bundles, over quantum affine algebras U-q(B-n((1))), U-q(D-n((1))) and U-q(D-n+1((2))), and show that the sets of all zigzag strip bundles for U-q(B-n((1))), U-q(D-n((1))) and U-q(D-n+1((2))) realize the crystal bases B(infinity) of U-q(-)(B-n((1))), U-q(-)(D-n((1))) and U-q(-)(D-n+1((2))), respectively. Further, we discuss the connection between zigzag strip bundle realization, Nakajima monomial realization, and polyhedral realization of the crystal B(infinity).
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Related Researcher
- Shin, Dong Uy
- COLLEGE OF EDUCATION (DEPARTMENT OF MATHEMATICS EDUCATION)