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.
2020 Mathematics Subject Classification:
Acknowledgments
The author would like to thank the anonymous referee sincerely for reading the paper carefully and giving valuable suggestions.