Hostname: page-component-77c89778f8-fv566 Total loading time: 0 Render date: 2024-07-21T06:35:08.342Z Has data issue: false hasContentIssue false
  • English
  • Français

Representations of the Twisted Heisenberg–Virasoro Algebra at Level Zero

Published online by Cambridge University Press:  20 November 2018

Yuly Billig
Yuly Billig*
Affiliation:
School of Mathematics and Statistics Carleton University 1125 Colonel By Drive Ottawa, Ontario K1S 5B6, email: billig@math.carleton.ca
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We describe the structure of the irreducible highest weight modules for the twisted Heisenberg–Virasoro Lie algebra at level zero. We prove that either a Verma module is irreducible or its maximal submodule is cyclic.

Keywords

17B6817B65
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 46 , Issue 4 , 01 December 2003 , pp. 529 - 537
Copyright
Copyright © Canadian Mathematical Society 2003

References

[ACKP] Arbarello, E., De Concini, C., Kac, V. G. and Procesi, C., Moduli spaces of curves and representation theory. Comm. Math. Phys. (1) 117 (1988), 1–36.Google Scholar
[BBS] Berman, S., Billig, Y. and Szmigielski, J., Vertex operator algebras and the representation theory of toroidal algebras. In: Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory, Contemp.Math. 297 (2002), 1–26.Google Scholar
[B1] Billig, Y., Principal vertex operator representations for toroidal Lie algebras. J. Math. Phys. (7) 39 (1998), 3844–3864.Google Scholar
[B2] Billig, Y., Energy-momentum tensor for the toroidal Lie algebras. Preprint, math.RT/0201313.Google Scholar
[EM] Rao, S. Eswara and Moody, R. V., Vertex representations for n-toroidal Lie algebras and a generalization of the Virasoro algebra. Comm. Math. Phys. (2) 159 (1994), 239–264.Google Scholar
[FM] Fabbri, M. and Moody, R. V., Irreducible representations of Virasoro-toroidal Lie algebras. Comm. Math. Phys. (1) 159 (1994), 1–13.Google Scholar