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Unitary Hecke algebra modules with nonzero Dirac cohomology

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Symmetry: Representation Theory and Its Applications

Part of the book series: Progress in Mathematics ((PM,volume 257))

Abstract

In this paper, we review the construction of the Dirac operator for graded affine Hecke algebras and calculate the Dirac cohomology of irreducible unitary modules for the graded Hecke algebra of gl(n).

To Nolan Wallach with admiration

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Notes

  1. 1.

    The first author was partially supported by NSF grants DMS-0967386, DMS-0901104 and an NSA-AMS grant. The second author was partially supported by NSF DMS-0968065 and NSA-AMS 081022.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    Dan Barbasch

  2. Mathematics Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, OX, 2666, Oxford, England

    Dan Ciubotaru

Authors
  1. Dan Barbasch
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  2. Dan Ciubotaru
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Corresponding author

Correspondence to Dan Barbasch .

Editor information

Editors and Affiliations

  1. Dept. Mathematics 442 Dunham Lab, Yale University, New Haven, Connecticut, USA

    Roger Howe

  2. Department of Mathematics, Baylor University, Waco, Texas, USA

    Markus Hunziker

  3. Department of Mathematical Sciences EMS Building, Room E403, University of Wisconsin, Milwaukee, Milwaukee, Wisconsin, USA

    Jeb F. Willenbring

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Barbasch, D., Ciubotaru, D. (2014). Unitary Hecke algebra modules with nonzero Dirac cohomology. In: Howe, R., Hunziker, M., Willenbring, J. (eds) Symmetry: Representation Theory and Its Applications. Progress in Mathematics, vol 257. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-1590-3_1

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