Glasnik Matematicki, Vol. 61, No. 1 (2026), 1-15. \( \)

AUBERT DUALS OF STRONGLY POSITIVE REPRESENTATIONS FOR METAPLECTIC GROUPS

Yeansu Kim and Gyujin Oh

Department of Mathematics Education, Chonnam National University, Gwangju 61186, Republic of Korea
e-mail:ykim@jnu.ac.kr

Department of Mathematics, Chonnam National University, Gwangju 61186, Republic of Korea
e-mail:lake2314@naver.com

Abstract.   We determine the Aubert duals of strongly positive representations of the metaplectic group \(\widetilde{Sp}(n)\) over a non-Archimedean local field \(F\) of characteristic different from two. Using the classification of Matić and an explicit analysis of Jacquet modules, we describe these duals in terms of precise inducing data. Our results extend known descriptions for classical groups to the metaplectic group case and clarify the role of Aubert duality for non-linear covering groups, providing a foundation for future applications to the study of unitary representations for these groups. Furthermore, we are able to show that the same method applies to odd general spin groups, yielding an explicit description of Aubert duals in that setting as well.

2020 Mathematics Subject Classification.   22E35, 22E50, 11F70

Key words and phrases.   Aubert duals, metaplectic groups, Jacquet modules

https://doi.org/10.3336/gm.61.1.01

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