Bosonic realizations of higher-level toroidal Lie algebras

• Autores: Naihuan Jing, Kailash C. Misra, Shaobin Tan
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 219, Nº 2, 2005, págs. 285-302
• Idioma: inglés
• DOI: 10.2140/pjm.2005.219.285
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• Resumen

  • We construct realizations for the 2-toroidal Lie algebra associated with the Lie algebra A1 using vertex operators based on bosonic elds. In particular our construction realizes higher-level representations of the 2-toroidal algebra for any given pair of levels (k0;k1) with k00. We also construct a smaller module of level (k0;0) for the toroidal algebra from the Fock space using certain screening vertex operator, and this later representation generalizes the higher-level construction of the ane Lie algebra 2.