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Representation Theory

Published by the American Mathematical Society, the Representation Theory (ERT) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.7.

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Geometric local theta correspondence for dual reductive pairs of type II at the Iwahori level
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by Banafsheh Farang-Hariri PDF
Represent. Theory 17 (2013), 610-646 Request permission


In this paper we are interested in the geometric local theta correspondence at the Iwahori level for dual reductive pairs $(G,H)$ of type II over a non-Archimedean field of characteristic $p\neq 2$ in the framework of the geometric Langlands program. We consider the geometric version of the $I_{H}\times I_{G}$-invariants of the Weil representation $\mathcal {S}^{I_{H}\times I_{G}}$ as a bimodule under the action of Iwahori-Hecke algebras $\mathcal {H}_{I_{G}}$ and $\mathcal {H}_{I_{H}}$ and we give some partial geometric description of the corresponding category under the action of Hecke functors. We also define geometric Jacquet functors for any connected reductive group $G$ at the Iwahori level and we show that they commute with the Hecke action of the $\mathcal {H}_{I_{L}}$-subelgebra of $\mathcal {H}_{I_{G}}$ for a Levi subgroup $L$.
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Additional Information
  • Banafsheh Farang-Hariri
  • Affiliation: Humboldt-Universitët zu Berlin, Institut für Mathematik, Unter den Linden 6, 10099 Berlin, Germany
  • Address at time of publication: Université de Paris XI, Laboratoire de Mathématiques, Bât 425, 91405 Orsay Cedex, France
  • Email:
  • Received by editor(s): February 26, 2013
  • Received by editor(s) in revised form: September 24, 2013
  • Published electronically: December 9, 2013
  • © Copyright 2013 American Mathematical Society
  • Journal: Represent. Theory 17 (2013), 610-646
  • MSC (2010): Primary 14D24, 11F27; Secondary 22E57, 20C08
  • DOI:
  • MathSciNet review: 3139267