Mathematische Zeitschrift

, Volume 288, Issue 1–2, pp 125–133 | Cite as

Iwahori component of the Gelfand–Graev representation

Article

Abstract

Let G be a split reductive group over a p-adic field F. Let B be a Borel subgroup and U the maximal unipotent subgroup of B. Let \(\psi \) be a Whittaker character of U. Let I be an Iwahori subgroup of G. We describe the Iwahori–Hecke algebra action on the Gelfand–Graev representation \((\mathrm {ind}_{U}^{G}\psi )^I\) by an explicit Hecke algebra module.

Notes

Acknowledgements

This work was initiated during the Sphericity 2016 Conference in Germany. The authors would like to thank the organizers for providing the excellent environment for discussions. Kei Yuen Chan was supported by the Croucher Postdoctoral Fellowship. Gordan Savin was supported in part by NSF Grant DMS-1359774.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Korteweg-de Vries Institute for MathematicsUniversiteit van AmsterdamAmsterdamThe Netherlands
  2. 2.Department of MathematicsUniversity of UtahSalt Lake CityUSA

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