Determinant and Character of W-infinity algebra

Abstract

We diagonalize the Hilbert space of some subclass of the quasifinite module of the \Winf algebra. States are classified according to their eigenvalues for infinitely many commuting charges and the Young diagrams. The parameter dependence of their norms is explicitly derived. The full character formulae of the degenerate representations are given as summation of the bilinear combinations of the Schur polynomials.

34 pages, YITP/K-1060, YITP/U-94-17, SULDP-1994-3 Improvement of the proofs of some theorems

References in corpus (10)

• Two Dimensional QCD is a String Theory
• 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
• Generalized Two-Dimensional QCD
• Eigensystem and Full Character Formula of the W_{1+infinity} Algebra with c=1
• Determinant Formulae of Quasi-Finite Representation of W_{1+\infty} Algebra at Lower Levels
• Unitary Representations of $W$ Infinity Algebras
• Free Fields and Quasi-Finite Representation of $W_{1+\infty }$ Algebra
• Subalgebras of $W_{1+\infty }$ and Their Quasifinite Representations

Cited by in corpus (14)

• Quantum W-symmetry in AdS_3
• W{1+ \infty} algebra, W_3 algebra, and Friedan-Martinec-Shenker bosonization
• On the tensionless limit of gauged WZW models
• Ghost Systems: A Vertex Algebra Point of View
• Universal two-parameter ${\mathcal{W}}_{\infty }$-algebra and vertex algebras of type $\mathcal{W}(2,3,\dots ,N)$
• W(1+infinity) algebra as a symmetry behind AGT relation
• Quantum toroidal algebras and solvable structures in gauge/string theory
• The structure of the Kac-Wang-Yan algebra
• Symmetry and Integrability of Non-Singlet Sectors in Matrix Quantum Mechanics
• Representation theory of the vertex algebra $W_{1+\infty }$
• Swimming of Microorganism and the String- and Membrane- like Algebra
• Representations of Centrally-Extended Lie Algebras over Differential Operators and Vertex Algebras
• Classification of Quasifinite Modules over the Lie Algebras of Weyl Type
• Etingof Trace, Path Hypergeometric Functions and Integrable Systems