Tight Monomials for Type G₂ and A₃

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.

Key Words:

• Canonical basis
• Quantum groups
• Tight monomials

2000 Mathematics Subject Classification:

• 17B37
• 16G20

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 [1].

This research is supported in part by NSFC Key Project no. 10631010.

Notes

Communicated by D. Nakano.