Stable conjugacy and epipelagic L-packets for Brylinski-Deligne covers of Sp(2n)

Abstract

Let $F$ be a local field of characteristic not $2$. We propose a definition of stable conjugacy for all the covering groups of $\mathrm{Sp}(2n,F)$ constructed by Brylinski and Deligne, whose degree we denote by $m$. To support this notion, we follow Kaletha's approach to construct genuine epipelagic $L$-packets for such covers in the non-archimedean case with $p\nmid 2m$, or some weaker variant when $4\mid m$; we also prove the stability of packets when $F\supset {\mathbb{Q}}_p$ with $p$ large. When $m=2$, the stable conjugacy reduces to that defined by J. Adams, and the epipelagic $L$-packets coincide with those obtained by $\Theta$-correspondence. This fits within Weissman's formalism of L-groups. For $n=1$ and $m$ even, it is also compatible with the transfer factors proposed by K. Hiraga and T. Ikeda.

92 pages, with an index. The new Section 10 is the Errata that fixes the mistakes in Sections 7.2 and 8.3 in the published version

References in corpus (1)

• Transfert d'intégrales orbitales pour le groupe métaplectique