Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting
Representation Theory
2008-10-11 v3
Abstract
We extend classical results of Kostant and 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
Cite
@article{arxiv.0704.3342,
title = {Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting},
author = {Victor G. Kac and Pierluigi Moseneder Frajria and Paolo Papi},
journal= {arXiv preprint arXiv:0704.3342},
year = {2008}
}
Comments
Latex file, 89 pages. Several misprints corrected. To appear in Advances in Mathematics