On character formulae for Weil representations for unitary groups over finite fields

Abstract

We calculate characters of Weil representations of unitary groups over finite fields geometrically. As a byproduct, we deduce another proof of Gérardin’s trace formula for the Weil representation. Our main ingredient is an explicit character formula for a special Fermat variety due to Hotta–Matsui.

Keywords:

• Character formula
• Fermat variety
• Weil representation

2020 Mathematics Subject Classification:

• Primary: 20C33
• Secondary: 11F27

Acknowledgments

The author would like to thank the anonymous referee sincerely for reading the paper carefully and giving valuable suggestions.

Additional information

Funding

This work was supported by JSPS KAKENHI Grant numbers 20K03529.