Eigensystem and Full Character Formula of the W_{1+infinity} Algebra with c=1

Abstract

By using the free field realizations, we analyze the representation theory of the W_{1+infinity} algebra with c=1. The eigenvectors for the Cartan subalgebra of W_{1+infinity} are parametrized by the Young diagrams, and explicitly written down by W_{1+infinity} generators. Moreover, their eigenvalues and full character formula are also obtained.

arXiv comment12 pages, YITP/K-1049, SULDP-1993-1, RIMS-959, Plain TEX, ( New references )

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• Determinant and Character of W-infinity algebra
• W(1+infinity) algebra as a symmetry behind AGT relation
• Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels
• The $W_{1+\infty }$ effective theory of the Calogero- Sutherland model and Luttinger systems.
• Free Fields and Quasi-Finite Representation of $W_{1+\infty }$ Algebra
• A string field theoretical description of (p,q) minimal superstrings
• Notes on the algebraic curves in (p,q) minimal string theory
• Quasifinite Highest Weight Modules over Super $W_{1+\infty }$ Algebra
• Tau-functions as highest weight vectors for W_{1+infty} algebra
• Subalgebras of $W_{1+\infty }$ and Their Quasifinite Representations
• Free fermions, KdV charges, generalised Gibbs ensembles and modular transforms
• Supermatrix models and multi ZZ-brane partition functions in minimal superstring theories
• Quantum dynamics of the effective field theory of the Calogero-Sutherland model
• Twisted vertex operators and Bernoulli polynomials
• Swimming of Microorganism and the String- and Membrane- like Algebra
• Quantum Mechanics for the Swimming of Micro-Organism in Two Dimensions