Mathematische Zeitschrift

, Volume 288, Issue 1–2, pp 415–437 | Cite as

A Miyawaki type lift for \(\textit{GSpin}(2,10)\)

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Abstract

Let \(\mathfrak {T}_2\) (resp. \(\mathfrak {T}\)) be the Hermitian symmetric domain of \(\textit{Spin}(2,10)\) (resp. \(E_{7,3}\)). In previous work (Compos. Math 152(2):223–254, 2016), we constructed holomorphic cusp forms on \(\mathfrak {T}\) from elliptic cusp forms with respect to \(\textit{SL}_2(\mathbb {Z})\). By using such cusp forms we construct holomorphic cusp forms on \(\mathfrak {T}_2\) which are similar to Miyawaki lift constructed by Ikeda (Duke Math J 131:469–497, 2006) in the context of symplectic groups. It is conditional on the conjectural Jacquet–Langlands correspondence from \(\textit{PGSO}(2,10)\) to \(\textit{PGSO}(6,6)\).

Keywords

Miyawaki type lift Langlands functoriality Ikeda lift Tube domain associated to orthogonal groups 

Mathematics Subject Classification

Primary 11F55 Secondary 11F70 22E55 20G41 

Notes

Acknowledgements

We would like to thank T. Ibukiyama, T. Ikeda, H. Katsurada, R. Lawther, A. Luzgarev, T. Moriyama and T. Sugano for their valuable comments. In particular Lawther sent very detailed notes [28] to us on the double coset decomposition in Sect. 4.1 and Luzgarev sent a mathematica code to the second author. Ikeda also pointed out several mistakes in a previous version. Without their help, this paper could not have been finished. Thanks are due to the referee who gave a very detailed report which pointed out several errors and helped us to clarify many points.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of TorontoTorontoCanada
  2. 2.Korea Institute for Advanced StudySeoulKorea
  3. 3.Mathematical InstituteTohoku UniversitySendaiJapan

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