Theta correspondence and Springer correspondence

Jia-Jun Ma; Congling Qiu; Zhiwei Yun; JiaLiang Zou

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arXiv · 2512.13020

Theta correspondence and Springer correspondence

Jia-Jun Ma·Congling Qiu·Zhiwei Yun·JiaLiang Zou

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Abstract

In this paper, we obtain an explicit formula for the theta correspondence of unipotent principal-series representations between an even orthogonal and a symplectic group or between general linear groups over a finite field. The formula is in terms of the Springer correspondence. Along the way we prove general results about module categories of Hecke categories arising from spherical varieties, and give a similar formula for the multiplicities of the unipotent principal series representations in the function space of the spherical variety in terms of relative Springer theory.

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BibTeX RIS

Jia-Jun Ma, Congling Qiu, Zhiwei Yun, JiaLiang Zou. 2025-12-16. Theta correspondence and Springer correspondence. https://arxiv.org/abs/2512.13020

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