Commutation of Transfer and Aubert-Zelevinski Involution for Metaplectic Groups

Abstract

A result of K. Hiraga [Compos. Math., 2004, 140(6): 1625–1656] says that endoscopic transfer is compatible with Aubert-Zelevinski involution. In this paper, we generalize Hiraga’s result to metaplectic group setting.

Keywords

Metaplectic group / endoscopy / 22E50 / 11F70

References

[1] Arthur J. The Endoscopic Classification of Representations—Orthogonal and Symplectic Groups. Amer. Math. Soc. Colloq. Publ., 61, 2013, Providence, RI, American Mathematical Society

[2] Aubert A-M. Dualité dans le groupe de Grothendieck de la catégorie des représentations lisses de longueur finie d’un groupe réductif p-adique. Trans. Amer. Math. Soc., 1995, 347(6): 2179-2189

[3] Hiraga K. On functoriality of Zelevinski involutions. Compos. Math., 2004, 140(6): 1625-1656

[4] Li W-W. Transfert d’intégrales orbitales pour le groupe métaplectique. Compos. Math., 2011, 147(2): 524-590

[5] Li W-W. Spectral transfer for metaplectic groups, I. Local character relations. J. Inst. Math. Jussieu, 2019, 18(1): 25-123

[6] Li W.-W., Stabilization of the trace formula for metaplectic groups. 2021, arXiv: 2109.06581

[7] Luo C. Howe finiteness conjecture for covering groups. Math. Res. Lett., 2017, 24(6): 1759-1774

[8] Xu B. On Mœglin’s parametrization of Arthur packets for p-adic quasisplit Sp(N) and SO(N). Canad. J. Math., 2017, 69(4): 890-960

[9] Xu B. On the cuspidal support of discrete series for p-adic quasisplit Sp(N) and SO(N). Manuscripta Math., 2017, 154(3–4): 441-502

Rights & permissions

Peking University