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Langlands parameters associated to special maximal parahoric spherical representations


Author: Manish Mishra
Journal: Proc. Amer. Math. Soc. 143 (2015), 1933-1941
MSC (2010): Primary 11R39, 20G05, 22E50
Published electronically: December 19, 2014
MathSciNet review: 3314103
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Abstract: We describe the image, under the local Langlands correspondence for tori, of the characters of a torus which are trivial on its Iwahori subgroup. Let $ k$ be a non-archimedian local field. Let $ \boldsymbol {G}$ be a connected reductive group defined over $ k$, which is quasi-split and split over a tamely ramified extension. Let $ K$ be a special maximal parahoric subgroup of $ \boldsymbol {G}(k)$. To the class of representations of $ \boldsymbol {G}(k)$ having a non-zero vector fixed under $ K$, we establish a bijection, in a natural way, with the twisted semisimple conjugacy classes of the inertia fixed subgroup of the dual group $ \hat {\boldsymbol {G}}$. These results generalize the well known classical results to the ramified case.


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Additional Information

Manish Mishra
Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel
Email: mmishra@math.huji.ac.il

DOI: https://doi.org/10.1090/S0002-9939-2014-12392-6
Received by editor(s): April 20, 2013
Received by editor(s) in revised form: October 15, 2013, and October 25, 2013
Published electronically: December 19, 2014
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2014 American Mathematical Society