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arXiv · 2511.14750

Covering Barbasch-Vogan duality and wavefront sets of genuine representations

Fan Gao·Baiying Liu·Chi-Heng Lo·Freydoon Shahidi
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Abstract

In this paper, we start by defining a covering Barbasch-Vogan duality and prove some of its properties. Then, for genuine representations of $p$-adic covering groups we formulate an upper bound conjecture for their wavefront sets using this covering Barbasch-Vogan duality and reduce it to anti-discrete representations. The formulation generalizes that of Ciubotaru-Kim and Hazeltine-Liu-Lo-Shahidi for linear algebraic groups. We prove this upper bound conjecture for Kazhdan-Patterson coverings of general linear groups.

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Fan Gao, Baiying Liu, Chi-Heng Lo, Freydoon Shahidi. 2025-11-18. Covering Barbasch-Vogan duality and wavefront sets of genuine representations. https://arxiv.org/abs/2511.14750

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