Mathematische Zeitschrift

, Volume 283, Issue 1–2, pp 169–196 | Cite as

Local theta correspondences between epipelagic supercuspidal representations

  • Hung Yean Loke
  • Jia-Jun Ma
  • Gordan Savin


In this paper we study the local theta correspondences between epipelagic supercupsidal representations of a type I classical dual pair \((G,G')\) over p-adic fields. We show that, besides an exceptional case, an epipelagic supercupsidal representation \(\pi \) of \({\widetilde{G}}\) lifts to an epipelagic supercupsidal representation \(\pi '\) of \({\widetilde{G}}'\) if and only if the epipelagic data of \(\pi \) and \(\pi '\) are related by the moment maps.


Local theta correspondence Stable vector Moment map Epipelagic supercuspidal representation 

Mathematics Subject Classification

22E46 22E47 



We would like to thank Wee Teck Gan and Jiu-Kang Yu for their valuable comments. Hung Yean Loke is supported by a MOE-NUS AcRF Tier 1 Grant R-146-000-208-112. Jia-Jun Ma is partially supported by ISF Grant 1138/10 during his postdoctoral Fellowship at Ben Gurion University and HKRGC Grant CUHK 405213 during his postdoctoral fellowship in IMS of CUHK. Gordan Savin is supported by an NSF Grant DMS-1359774.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Department of MathematicsNational University of SingaporeSingaporeSingapore
  2. 2.The Institute of Mathematical SciencesThe Chinese University of Hong KongShatinHong Kong
  3. 3.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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