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Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting |
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| Authors: | Victor G Kac |
| Institution: | a Department of Mathematics, Rm 2-178, MIT, 77 Mass. Ave, Cambridge, MA 02139, USA b Politecnico di Milano, Polo regionale di Como, Via Valleggio 11, 22100 Como, Italy c Dipartimento di Matematica, Università di Roma “La Sapienza”, P.le A. Moro 2, 00185, Roma, Italy |
| Abstract: | We extend classical results of Kostant et al. on multiplets of representations of finite-dimensional Lie algebras and on the cubic Dirac operator to the setting of affine Lie algebras and twisted affine cubic Dirac operator. We prove in this setting an analogue of Vogan's conjecture on infinitesimal characters of Harish-Chandra modules in terms of Dirac cohomology. For our calculations we use the machinery of Lie conformal and vertex algebras. |
| Keywords: | Multiplets of representations Affine algebras Dirac operator Vertex algebras |
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