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

References

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

[2] AubertA-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] HiragaK. On functoriality of Zelevinski involutions. Compos. Math., 2004, 140(6): 1625-1656

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

[5] LiW-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] LuoC. Howe finiteness conjecture for covering groups. Math. Res. Lett., 2017, 24(6): 1759-1774

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

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Peking University