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The Dirac cohomology of a finite dimensional representation


Authors: S. Mehdi and R. Zierau
Journal: Proc. Amer. Math. Soc. 142 (2014), 1507-1512
MSC (2010): Primary 17B45, 20G05
Published electronically: February 10, 2014
MathSciNet review: 3168458
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Abstract: The Dirac cohomology of a finite dimensional representation of a complex semisimple Lie algebra $ \mathfrak{g}$, with respect to any quadratic subalgebra $ \mathfrak{h}$, is computed. This generalizes a formula obtained by Kostant in the case where $ \mathfrak{g}$ and $ \mathfrak{h}$ have equal rank, and by Huang, Kang and Pandžić in the case where $ \mathfrak{h}$ is the fixed point of an involution.


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Additional Information

S. Mehdi
Affiliation: Département de Mathématiques, Université de Metz - CNRS, F-57045 Metz Cedex 1, France
Address at time of publication: Institut Elie Cartan de Lorraine, UMR 7502 - CNRS, Université de Lorraine, F-57045 Metz Cedex 1, France
Email: salah.mehdi@univ-lorraine.fr

R. Zierau
Affiliation: Department of Mathematics, Oklahoma State University, Stillwater, Oklahoma 74078
Email: zierau@math.okstate.edu

DOI: https://doi.org/10.1090/S0002-9939-2014-11952-6
Received by editor(s): July 18, 2011
Received by editor(s) in revised form: June 4, 2012
Published electronically: February 10, 2014
Communicated by: Kailash C. Misra
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.