Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Uniqueness

Yao Cheng

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arXiv · 2510.03068

Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Uniqueness

Yao Cheng

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Abstract

The conjectural theory of local newofmrs for the split $p$-adic group ${\rm SO}_{2n+1}$, proposed by Gross, predicts that the space of local newforms in a generic representation is one-dimensional. In this note, we prove that this space is at most one-dimensional and verify its expected arithmetic properties, conditional on existence. These results play an important role in our proof of the existence part of the newform conjecture.

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BibTeX RIS

Yao Cheng. 2025-10-03. Local newforms for generic representations of $p$-adic ${\rm SO}_{2n+1}$: Uniqueness. https://arxiv.org/abs/2510.03068

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