Spectral transfer for metaplectic groups. II. Hecke algebra correspondences

Abstract

Let $\mathrm{Mp}(2n)$ be the metaplectic group over a local field $F\supset {\mathbb{Q}}_p$ defined by an additive character of $F$ of conductor $4{\mathfrak{o}}_F$. Gan-Savin ($p\ne 2$) and Takeda-Wood ($p=2$) obtained an equivalence between the Bernstein block of $\mathrm{Mp}(2n)$ containing the even (resp. odd) Weil representation and the Iwahori-spherical block of the split $\mathrm{SO}(2n+1)$ (resp. its non-split inner form), by giving an isomorphism between Hecke algebras. We revisit this equivalence from an endoscopic perspective. It turns out that the L-parameters of irreducible representations are preserved, whilst the difference between characters of component groups is governed by symplectic local root numbers.

32 pages. Published version

References in corpus (3)

• Transfert d'intégrales orbitales pour le groupe métaplectique
• Local intertwining relation for metaplectic groups
• Hecke Algebra Correspondences for the metaplectic group