On Lepowsky-Wilson's Z-algebra

2000/05/22 by Y. Hara, M. Jimbo, H. Konno +2
Mathematics · Physics and Astronomy · #math.QA #math-ph #math.MP

paper · pdf

published as Recent Developments in Infinite-Diminsional Lie Algebras and Conformal Field Theory, Proceedings of the Conference on Infinite-dimensional Lie Theory, Contemporary Mathematics 297, AMS, Providence, 2002. · 8 pages

arxiv created 2000/05/22 · arxiv updated 2009/11/30

Abstract

We show that the deformed Virasoro algebra specializes in a certain limit to Lepowsky-Wilson's Z-algebra. This leads to a free field realization of the affine Lie algebra sl₂ which respects the principal gradation. We discuss some features of this bosonization including the screening current and vertex operators.

Related

• On vertex algebra representations of the Schrödinger-Virasoro Lie algebra
• Bosonization of ZF Algebras: Direction Toward Deformed Virasoro Algebra
• Approximate representations and Virasoro algebra
• Free Boson Representation of U_q(sl₂)
• Massless XXZ Model and Degeneration of the Elliptic Algebra A_q,p(\widehatsl₂)