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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On Demazure crystals for $ U_q(G_2^{(1)})$


Authors: Rebecca L. Jayne and Kailash C. Misra
Journal: Proc. Amer. Math. Soc. 139 (2011), 2343-2356
MSC (2010): Primary 17B37, 17B10; Secondary 17B67
Published electronically: December 7, 2010
MathSciNet review: 2784799
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Abstract: We show that there exist suitable sequences $ \{w^{(k)}\}_{k \ge 0}$ and $ \{w'^{(k)}\}_{k \ge 0}$ of Weyl group elements for a given perfect crystal of level $ l\ge 1$ such that the path realizations of the Demazure crystals $ B_{w^{(k)}}(l\Lambda_0)$ and $ B_{w'^{(k)}}(l\Lambda_2)$ for the quantum affine algebra $ U_q(G_2^{(1)})$ have tensor-product-like structures with mixing index $ \kappa =1$.


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Additional Information

Rebecca L. Jayne
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
Email: rljayne@unity.ncsu.edu

Kailash C. Misra
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695-8205
Email: misra@math.ncsu.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10663-9
PII: S 0002-9939(2010)10663-9
Received by editor(s): March 31, 2010
Received by editor(s) in revised form: June 11, 2010, and June 23, 2010
Published electronically: December 7, 2010
Additional Notes: This work was partially supported by NSA grant H98230-08-1-0080.
Communicated by: Gail R. Letzter
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.