Unitary representations of the Virasoro algebra and a conjecture of Kac

Vyjayanthi Chari; Andrew Pressley

Compositio Mathematica (1988)

  • Volume: 67, Issue: 3, page 315-342
  • ISSN: 0010-437X

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Chari, Vyjayanthi, and Pressley, Andrew. "Unitary representations of the Virasoro algebra and a conjecture of Kac." Compositio Mathematica 67.3 (1988): 315-342. <http://eudml.org/doc/89921>.

@article{Chari1988,
author = {Chari, Vyjayanthi, Pressley, Andrew},
journal = {Compositio Mathematica},
keywords = {Ramond superalgebra; unitary representations; Virasoro algebra; Neveu- Schwarz Lie superalgebra},
language = {eng},
number = {3},
pages = {315-342},
publisher = {Kluwer Academic Publishers},
title = {Unitary representations of the Virasoro algebra and a conjecture of Kac},
url = {http://eudml.org/doc/89921},
volume = {67},
year = {1988},
}

TY - JOUR
AU - Chari, Vyjayanthi
AU - Pressley, Andrew
TI - Unitary representations of the Virasoro algebra and a conjecture of Kac
JO - Compositio Mathematica
PY - 1988
PB - Kluwer Academic Publishers
VL - 67
IS - 3
SP - 315
EP - 342
LA - eng
KW - Ramond superalgebra; unitary representations; Virasoro algebra; Neveu- Schwarz Lie superalgebra
UR - http://eudml.org/doc/89921
ER -

References

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  2. 2 D. Friedan, Z. Qiu and S. Shenker, Superconformal invariance in two dimensions and the tricritical Ising model, Phys. Lett.151 B (1985) 37-43. MR778509
  3. 3 D. Friedan, Z. Qiu and S. Shenker, Details of the non-unitarity proof for highest weight representations of the Virasoro algebra, Commun. Math. Phys.107 (1986) 535-542. Zbl0608.17010MR868732
  4. 4 P. Goddard, A. Kent and D. Olive, Virasoro algebras and coset space models, Phys. Lett.152B (1985) 88-93. Zbl0661.17015MR778819
  5. 5 P. Goddard, A. Kent and D. Olive, Unitary representations of the Virasoro and super-Virasoro algebras, Commun. Math. Phys.103 (1986) 105-119. Zbl0588.17014MR826859
  6. 6 V.G. Kac, Lie superalgebras, Advances in Math.26 (1977) 8-96. Zbl0366.17012MR486011
  7. 7 V.G. Kac, Highest weight representations of infinite-dimensional Lie algebras. Proceedings of the International Congress of Mathematicians (Helsinki, 1978), 299-304, Acad. Sci. Fennica, Helsinki (1980). Zbl0425.17009MR562619
  8. 8 V.G. Kac, Some problems of infinite-dimensional Lie algebras and their representations. Lie algebras and related topics, 117-126, Lecture Notes in Mathematics, 933, Springer (1982). Zbl0493.17011MR675110
  9. 9 V.G. Kac and M. Wakimoto, Unitarizable highest weight representations of the Virasoro, Neveu-Schwarz and Ramond algebras. Conformal groups and related symmetries: physical results and mathematical background, 345-371, Lecture Notes in Physics, 261, Springer, 1986. MR870235
  10. 10 I. Kaplansky, The Virasoro algebra, Commun. Math. Phys.86 (1982) 49-54. Zbl0515.17007MR678001
  11. 11 I. Kaplansky and L.J. Santharoubane, Harish Chandra modules over the Virasoro algebra. Infinite-dimensional groups with applications, 217-231, MSRI Publications No. 5, Springer (1985). Zbl0589.17013MR823321
  12. 12 A.A. Kirillov, Unitary representations of the group of diffeomorphisms and of some of its subgroups, Selecta Math. Soviet.1 (1981) 351-372. Zbl0515.58009MR697287
  13. 13 A.W. Knapp, Representation theory of semisimple groups, Princeton University Press, Princeton (1986). Zbl0604.22001MR855239
  14. 14 I.A. Kostrikin, Irreducible graded representations of Lie algebras of Cartan type, Soviet Math. Dokl.19 (1978) 1369-1371. Zbl0412.17013
  15. 15 R.P. Langlands, On unitary representations of the Virasoro algebra. Proceedings of the Montreal workshop on infinite-dimensional Lie algebras and their applications, S. Kass, ed., to appear. Zbl0748.17025MR1114998
  16. 16 A. Tsuchiya and Y. Kanie, Unitary representations of the Virasoro algebra, Duke Math. J.53 (1986) 1013-1046. Zbl0611.17005MR874679
  17. 17 D.A. Vogan, Jr., Representations of real reductive Lie groups. Progress in Mathematics15, Birkhäuser, Boston (1981). Zbl0469.22012MR632407
  18. 18 E.T. Whittaker and G.N. Watson, A course of modern analysis, 4th edition, Cambridge University Press, Cambridge (1978). Zbl45.0433.02MR1424469JFM45.0433.02

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