Abstract
We prove a conjecture of Udo Riese about the minimal ring of definition for principal series Weil characters of , for p an odd prime. More precisely, we show that the -dimensional Weil characters can be realized over the ring of integers of , where , and we provide explicit integral models over these quadratic rings. We do so by studying the Galois action on the integral models of Weil characters recently discovered by Yilong Wang.
Acknowledgments
We would like to thank Siu-Hung Ng, Yilong Wang and Shaul Zemel for sharing many great ideas and conversations about this problem, as well as the referee for many insightful comments.