Character and determinant formulae of quasifinite representation of theW 1+∞ algebra

1994/05/31 by Hidetoshi Awata, H. Awata, Masafumi Fukuma +5 · 26 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Algebraic structures and combinatorial models #Bilinear form #Bilinear interpolation #Character (mathematics) #Degenerate energy levels #Eigenvalues and eigenvectors #Geometry #Hilbert space #Law #Mathematics #Nonlinear Waves and Solitons #Physics #Pure mathematics #Representation (politics) #Statistics #hep-th

paper · pdf · doi:10.1007/bf02099433

published in Communications in Mathematical Physics 172(2), 377-400 (Springer Science+Business Media) · 34 pages, YITP/K-1060, YITP/U-94-17, SULDP-1994-3 Improvement of the proofs of some theorems

arxiv created 1994/09/20 · openalex publication_date 1995/09/01 · arxiv updated 2014/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

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.

Citations

• Eigensystem and full character formula of theW 1+? algebra withc = 1
• Determinant formulae of quasi-finite representation of W1+∞ algebra at lower levels
• Infinite conformal symmetry in two-dimensional quantum field theory
• UNITARY REPRESENTATIONS OF W INFINITY ALGEBRAS
• Two-dimensional QCD is a string theory
• Free fields and quasi-finite representation of 1+∞ algebra

Cited by

• The Structure of the Kac–Wang–Yan Algebra
• \W\/ Algebra, \Wth Algebra, and Friedan-Martinec-Shenker Bosonization