Differential equations in vertex algebras and simple modules for the Lie algebra of vector fields on a torus

• Autores: Yuly Billig, Alexander Molev, Ruibin Zhang
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 218, Nº 6, 2008, págs. 1972-2004
• Idioma: inglés
• DOI: 10.1016/j.aim.2008.03.026
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• Resumen

  • We study irreducible representations for the Lie algebra of vector fields on a 2-dimensional torus constructed using the generalized Verma modules. We show that for a certain choice of parameters these representations remain irreducible when restricted to a loop subalgebra in the Lie algebra of vector fields. We prove this result by studying vertex algebras associated with the Lie algebra of vector fields on a torus and solving non-commutative differential equations that we derive using the vertex algebra technique