Abstract
The global crystal basis or canonical basis plays an important role in the theory of the quantum groups and their representations. The tight monomials are the simplest elements in the canonical basis. Based on Reineke, Deng, and Du's work, the tight monomials in quantized enveloping algebra of type G2 and A3 are completely determined in this article.
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ACKNOWLEDGMENTS
I would like to thank my supervisor Jianpan Wang for his guidance in my study and in the preparation of the article. I want also to express my special thanks to Jie Du and Bangming Deng for kindly showing me their preprint [Citation1].
This research is supported in part by NSFC Key Project no. 10631010.
Notes
Communicated by D. Nakano.