Spherical representations of unitary groups at ramified places and the arithmetic inner product formula

Zhuoni Chi

Spherical representations of unitary groups at ramified places and the arithmetic inner product formula

Number Theory 2026-05-21 v2 Algebraic Geometry Representation Theory

Authors: Zhuoni Chi

Abstract

In this article, we study admissible representations of even unitary groups over local fields, where the quadratic extension is ramified, with invariant vectors under the action of the stabilizer of a unimodular lattice and some properties of the corresponding integral model of unitary Shimura varieties. As a direct application, we are able to improve the arithmetic inner product formula so that the places with local root number $(-1)$ are allowed to be ramified.

Keywords

unitary groups ramified places spherical representations arithmetic inner product Shimura varieties

Cite

@article{arxiv.2602.02492,
  title  = {Spherical representations of unitary groups at ramified places and the arithmetic inner product formula},
  author = {Zhuoni Chi},
  journal= {arXiv preprint arXiv:2602.02492},
  year   = {2026}
}

Comments

74 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2006.06139, arXiv:2101.09485 by other authors

Spherical representations of unitary groups at ramified places and the arithmetic inner product formula

Abstract

Keywords

Cite

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