Free Fields and Quasi-Finite Representation of $W_{1+\infty }$ Algebra

Abstract

We study quasi-finite representation of the $\Winf$ algebra recently proposed by Kac and Radul. When the central charge is integer, we show that they are represented by free fermions and bosonic ghosts. There are some nontrivial representations with vanishing central charge. We discuss that they may be described by large $N$ limit of topological models. We calculate their operator algebras explicitly.

10 pages, UT-661, harvmac Reference is corrected

References in corpus (6)

• Quasifinite highest weight modules over the Lie algebra of differential operators on the circle
• Infinite Symmetry in the Quantum Hall Effect
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Interaction of Discrete States in Two-Dimensional String Theory
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Cited by in corpus (13)

• W_{1+\infty} and W(gl_N) with central charge N
• Collective fields, Calogero-Sutherland model and generalized matrix models
• On the tensionless limit of gauged WZW models
• Bosonic ghostbusting -- The bosonic ghost vertex algebra admits a logarithmic module category with rigid fusion
• Determinant and Character of W-infinity algebra
• Eigensystem and Full Character Formula of the W_{1+infinity} Algebra with c=1
• W(1+infinity) algebra as a symmetry behind AGT relation
• Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels
• Quasifinite Highest Weight Modules over Super $W_{1+\infty }$ Algebra
• Subalgebras of $W_{1+\infty }$ and Their Quasifinite Representations
• Multilocal bosonization
• Quantum Mechanics for the Swimming of Micro-Organism in Two Dimensions
• Free Field realization of the ${\hat{\mathcal{D}}}_q$ Algebra for the $\eta$-$\xi$ system, Integrals of Motion and Characters