Dirac Cohomology for Lie Superalgebras |
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| Authors: | Jing-Song Huang Pavle Pandžić |
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| Affiliation: | (1) Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong SAR, China;(2) Department of Mathematics, University of Zagreb, Bijenicka 30, PP 335, 10002 Zagreb, Croatia |
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| Abstract: | Dirac cohomology is a new tool to study representations of semisimple Lie groups and Lie algebras. The aim of this paper is to define a Dirac operator for a Lie superalgebra of Riemannian type and show that this Dirac operator has similar nature as the one for semisimple Lie algebras. As a consequence, we show how to determine the infinitesimal character of a representation by the infinitesimal character of its Dirac cohomology. |
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