Dirac cohomology of one-$W$-type representations
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- by Dan Ciubotaru and Allen Moy PDF
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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.References
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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
- MR Author ID: 754534
- 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
- MR Author ID: 127665
- Email: amoy@ust.hk
- 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
- © Copyright 2014 American Mathematical Society
- 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
- MathSciNet review: 3293718