Minimal integral models for principal series Weil characters

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.