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

Wen Wei Li

• Let F be a local field of characteristic not 2. We propose a definition of stable conjugacy for all the covering groups of \text {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 \not \mid 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.