Supercharacter theories for Sylow p-subgroups of Lie type G₂

Abstract

We construct a supercharacter theory, and establish the supercharacter table for Sylow p-subgroups $G_2^{syl}\left(q\right)$ of the Chevalley groups $G_2\left(q\right)$ of Lie type $G_2$ when p>2. Then we calculate the conjugacy classes, determine the complex irreducible characters by Clifford theory, and obtain the character tables for $G_2^{syl}\left(q\right)$ when p>3.

Keywords:

• Supercharacter theory
• character table
• Sylow p-subgroup

2010 Mathematics Subject Classifications:

• Primary 20C15
• 20D15. Secondary 20C33
• 20D20

Acknowledgments

This paper is a part of my PhD thesis [34] at the University of Stuttgart, Germany, so I am deeply grateful to my supervisor Richard Dipper. I also would like to thank Jun Hu, Markus Jedlitschky and Mathias Werth for the helpful discussions and valuable suggestions.

Disclosure statement

No potential conflict of interest was reported by the author.

Additional information

Funding

This paper is supported by the National Natural Science Foundation of China (No. 11525102).