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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: [email protected]
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Abstract

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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