Aubert duals of strongly positive representations for metaplectic groups

TL;DR

This paper explicitly determines the Aubert duals of strongly positive representations for metaplectic groups over non-Archimedean fields, extending classical group results and clarifying duality roles in non-linear coverings.

Contribution

It provides a new explicit description of Aubert duals for metaplectic groups and odd GSpin groups, expanding the understanding of duality in non-linear covering groups.

Findings

Explicit description of Aubert duals for metaplectic groups

Extension of classical group duality results to covering groups

Application of methods to odd GSpin groups

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 Mati\'c 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 groups 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 those cases. Furthermore, We are able to show that the same method applies to odd general spin groups $GSpin(2n+1)$, yielding an explicit description of Aubert duals in that setting as well.