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Dirac cohomology of one-$ W$-type representations


Authors: Dan Ciubotaru and Allen Moy
Journal: Proc. Amer. Math. Soc. 143 (2015), 1001-1013
MSC (2010): Primary 20C08, 22E50
DOI: https://doi.org/10.1090/S0002-9939-2014-12303-3
Published electronically: November 12, 2014
MathSciNet review: 3293718
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Abstract: The smooth hermitian representations of a split reductive $ p$-adic group whose restriction to a maximal hyperspecial compact subgroup contain a single $ K$-type with Iwahori fixed vectors have been studied in a paper by Barbasch and Moy (1999) in the more general setting of modules for graded affine Hecke algebras with parameters. We show that every such one $ K$-type module has nonzero Dirac cohomology (in the sense of a paper by Barbasch, Ciubotaru and Trapa), and use Dirac operator techniques to determine the semisimple part of the Langlands parameter for these modules, thus completing their classification.


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Additional Information

Dan Ciubotaru
Affiliation: Department of Mathematics, University of Utah, Salt Lake City, Utah 84112
Address at time of publication: Mathematical Institute, University of Oxford, Oxford, OX26GG, UK
Email: ciubo@math.utah.edu, dan.ciubotaru@maths.ox.ac.uk

Allen Moy
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
Email: amoy@ust.hk

DOI: https://doi.org/10.1090/S0002-9939-2014-12303-3
Received by editor(s): August 23, 2012
Received by editor(s) in revised form: July 6, 2013
Published electronically: November 12, 2014
Additional Notes: This paper was partly written while the first author visited Hong Kong University of Science and Technology. The first author thanks Xuhua He and the Department of Mathematics for their invitation and hospitality
The authors were supported in part by NSF-DMS 0968065 and Hong Kong Research Grants Council grant CERG #602408.
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2014 American Mathematical Society