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arXiv · 2110.14556

Minimal Integral Models for Principal Series Weil Characters

Luca Candelori·Yatin Patel
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Abstract

We prove a conjecture of Udo Riese about the minimal ring of definition for principal series Weil characters of $\text{SL}_2(\mathbb{F}_p)$, for $p$ an odd prime. More precisely, we show that the $(p+1)/2$-dimensional Weil characters can be realized over the ring of integers of $\mathbb{Q}(\sqrt{\varepsilon p})$, where $\varepsilon =(-1)^{(p-1)/2}$, 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.

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Luca Candelori, Yatin Patel. 2021-10-27. Minimal Integral Models for Principal Series Weil Characters. https://arxiv.org/abs/2110.14556

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