Stable vectors in dual Vinberg representations of $F_4$

Beth Romano

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arXiv · 2107.10305

Stable vectors in dual Vinberg representations of $F_4$

Beth Romano

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Abstract

This paper gives a classification of stable vectors in dual Vinberg representations coming from a graded Lie algebra of type $F_4$ in a way that is independent of the field of definition. Relating these gradings to Moy-Prasad filtrations, we obtain the input for Reeder-Yu's construction of epipelagic supercuspidal representations. As a corollary, this construction gives new supercuspidal representations of $F_4(\mathbb{Q}_p)$ when $p$ is small.

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Beth Romano. 2021-07-21. Stable vectors in dual Vinberg representations of $F_4$. https://arxiv.org/abs/2107.10305

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