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Symmetry, Integrability and Geometry: Methods and Applications, 2010, Volume 6, 022, 12 pp.
DOI: https://doi.org/10.3842/SIGMA.2010.022 (Mi sigma479) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Zero Action on Perfect Crystals for $U_q(G_2^{(1)})$

Kailash C. Misraa, Mahathir Mohamadb, Masato Okadob

a Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205, USA
b Department of Mathematical Science, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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DOI: https://doi.org/10.3842/SIGMA.2010.022
Abstract: The actions of 0-Kashiwara operators on the $U'_q(G_2^{(1)})$-crystal $B_l$ in [Yamane S., J. Algebra 210 (1998), 440–486] are made explicit by using a similarity technique from that of a $U'_q(D_4^{(3)})$-crystal. It is shown that $\{B_l\}_{l\ge1}$ forms a coherent family of perfect crystals.
Keywords: combinatorial representation theory; quantum affine algebra; crystal bases.
Received: November 13, 2009; in final form March 3, 2010; Published online March 9, 2010
Bibliographic databases:
Document Type: Article
MSC: 05E99; 17B37; 17B67; 81R10; 81R50
Language: English
Citation: Kailash C. Misra, Mahathir Mohamad, Masato Okado, “Zero Action on Perfect Crystals for $U_q(G_2^{(1)})$”, SIGMA, 6 (2010), 022, 12 pp.
Citation in format AMSBIB
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\paper Zero Action on Perfect Crystals for $U_q(G_2^{(1)})$
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\papernumber 022
\totalpages 12
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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