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. (C) 2007 Elsevier Inc. All rights reserved.
Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting / Papi, Paolo; P., Moseneder Frajria; Victor G., Kac. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - STAMPA. - 217:6(2008), pp. 2485-2562. [10.1016/j.aim.2007.10.005]
Multiplets of representations, twisted Dirac operators and Vogan's conjecture in affine setting
PAPI, Paolo;
2008
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. (C) 2007 Elsevier Inc. All rights reserved.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
