Dirac cohomology, unitary representations and a proof of a conjecture of Vogan |
| |
Authors: | Jing-Song Huang Pavle Pandzic |
| |
Institution: | Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong ; Department of Mathematics, University of Zagreb, PP 335, 10002 Zagreb, Croatia |
| |
Abstract: | Let be a connected semisimple Lie group with finite center. Let be the maximal compact subgroup of corresponding to a fixed Cartan involution . We prove a conjecture of Vogan which says that if the Dirac cohomology of an irreducible unitary -module contains a -type with highest weight , then has infinitesimal character . Here is the half sum of the compact positive roots. As an application of the main result we classify irreducible unitary -modules with non-zero Dirac cohomology, provided has a strongly regular infinitesimal character. We also mention a generalization to the setting of Kostant's cubic Dirac operator. |
| |
Keywords: | Dirac operator cohomology unitary representation infinitesimal character |
|
| 点击此处可从《Journal of the American Mathematical Society》浏览原始摘要信息 |
| 点击此处可从《Journal of the American Mathematical Society》下载免费的PDF全文 |