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arXiv · 2410.16564

Conductors and local newforms for the metaplectic group of rank 1

Hiroshi Ishimoto
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Abstract

In an earlier paper of W. Casselman, the theory of local newforms and conductors was initiated. Later, Roberts and Schmidt studied local newforms for the metaplectic group of rank 1. In this paper we define and calculate conductors of irreducible genuine representations of the metaplectic group of rank 1 over non-archimedean local field of characteristic zero and of odd residual characteristic. Moreover, we shall give an explicit formulae for dimensions of spaces of local newforms, and show a compatibility with the local theta correspondence.

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Hiroshi Ishimoto. 2024-10-21. Conductors and local newforms for the metaplectic group of rank 1. https://arxiv.org/abs/2410.16564

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