Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 022, 12 pages      arXiv:0911.2579      http://dx.doi.org/10.3842/SIGMA.2010.022
Contribution to the Proceedings of the Workshop “Geometric Aspects of Discrete and Ultra-Discrete Integrable Systems”

Zero Action on Perfect Crystals for Uq(G2(1))

Kailash C. Misra a, Mahathir Mohamad b and Masato Okado b
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

Received November 13, 2009, in final form March 03, 2010; Published online March 09, 2010

Abstract
The actions of 0-Kashiwara operators on the Uq'(G2(1))-crystal Bl in [Yamane S., J. Algebra 210 (1998), 440-486] are made explicit by using a similarity technique from that of a Uq'(D4(3))-crystal. It is shown that {Bl}l ≥ 1 forms a coherent family of perfect crystals.

Key words: combinatorial representation theory; quantum affine algebra; crystal bases.

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References

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  7. Yamane S., Perfect crystals of Uq(G2(1)), J. Algebra 210 (1998), 440-486, q-alg/9712012.

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