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arXiv · 2510.22460

The MVW involution of the metaplectic group

Shuichiro Takeda·Justin Trias
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Abstract

The MVW involution -- named after Colette Moeglin, Marie-France Vignéras, and Jean-Loup Waldspurger -- is a fundamental dualizing involution in the representation theory of $p$-adic classical groups. It extends the well-known transpose-inverse automorphism for general linear groups. In this work, we establish the existence of the MVW involution for the metaplectic group over a non-archimedean local field $F$ of characteristic different from $2$ and with residue characteristic $p$. Our construction applies to representations over any coefficient field of characteristic distinct from $p$.

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Shuichiro Takeda, Justin Trias. 2025-10-25. The MVW involution of the metaplectic group. https://arxiv.org/abs/2510.22460

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