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Dirac Cohomology of some Harish-Chandra Modules

Authors:	Jing-Song Huang Yi-Fang Kang Pavle Pandžić

Institution:	(1) Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China;(2) Department of Mathematics, Tianjin University, Tianjin, China;(3) Department of Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia

Abstract:	In this paper we determine the Dirac cohomology of certain irreducible Harish-Chandra modules of a semisimple connected Lie group G with finite center: irreducible finite-dimensional modules and unitary A $\mathfrak{q}$ (λ) modules. We also comment on the relationship to ( $\mathfrak{g}$ , K)-cohomology. The first named author is partially supported by research grants from RGC of Hong Kong SAR and NSF of China. The second named author is partially supported by the National Natural Science Foundation of China (10501025), Liu Hui Center for Applied Mathematics and Youth Teachers Foundation of Tianjin University. The third named author is partially supported by a grant from the Ministry of Science, Education and Sports of the Republic of Croatia.

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