Simple Virasoro modules induced from codimension one subalgebras of the positive part

Mazorchuk, Volodymyr; Wiesner, Emilie

doi:10.1090/S0002-9939-2014-12098-3

Simple Virasoro modules induced from codimension one subalgebras of the positive part
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by Volodymyr Mazorchuk and Emilie Wiesner PDF

Proc. Amer. Math. Soc. 142 (2014), 3695-3703 Request permission

Abstract:

We construct a new five-parameter family of simple modules over the Virasoro algebra.

References

Punita Batra and Volodymyr Mazorchuk, Blocks and modules for Whittaker pairs, J. Pure Appl. Algebra 215 (2011), no. 7, 1552–1568. MR 2771629, DOI 10.1016/j.jpaa.2010.09.010
Charles H. Conley and Christiane Martin, A family of irreducible representations of the Witt Lie algebra with infinite-dimensional weight spaces, Compositio Math. 128 (2001), no. 2, 153–175. MR 1850181, DOI 10.1023/A:1017566220585
B. L. Feĭgin and D. B. Fuks, Verma modules over a Virasoro algebra, Funktsional. Anal. i Prilozhen. 17 (1983), no. 3, 91–92. MR 714236
Xiangqian Guo, Rencai Lu, and Kaiming Zhao, Fraction representations and highest-weight-like representations of the Virasoro algebra, J. Algebra 387 (2013), 68–86. MR 3056686, DOI 10.1016/j.jalgebra.2013.04.012
Kenji Iohara and Yoshiyuki Koga, Representation theory of the Virasoro algebra, Springer Monographs in Mathematics, Springer-Verlag London, Ltd., London, 2011. MR 2744610, DOI 10.1007/978-0-85729-160-8
V. G. Kac and A. K. Raina, Bombay lectures on highest weight representations of infinite-dimensional Lie algebras, Advanced Series in Mathematical Physics, vol. 2, World Scientific Publishing Co., Inc., Teaneck, NJ, 1987. MR 1021978
R. Lü, K. Zhao; Irreducible Virasoro modules from irreducible Weyl modules. J. Algebra, to appear.
Rencai Lü, Xiangqian Guo, and Kaiming Zhao, Irreducible modules over the Virasoro algebra, Doc. Math. 16 (2011), 709–721. MR 2861395
Olivier Mathieu, Classification of Harish-Chandra modules over the Virasoro Lie algebra, Invent. Math. 107 (1992), no. 2, 225–234. MR 1144422, DOI 10.1007/BF01231888
Volodymyr Mazorchuk and Kaiming Zhao, Classification of simple weight Virasoro modules with a finite-dimensional weight space, J. Algebra 307 (2007), no. 1, 209–214. MR 2278050, DOI 10.1016/j.jalgebra.2006.05.007
V. Mazorchuk, K. Zhao; Simple Virasoro modules which are locally finite over a positive part. Selecta Math. (N.S.), to appear.
Matthew Ondrus and Emilie Wiesner, Whittaker modules for the Virasoro algebra, J. Algebra Appl. 8 (2009), no. 3, 363–377. MR 2535995, DOI 10.1142/S0219498809003370
Hechun Zhang, A class of representations over the Virasoro algebra, J. Algebra 190 (1997), no. 1, 1–10. MR 1442144, DOI 10.1006/jabr.1996.6565