Coset construction

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In mathematics, the coset construction (or GKO construction) is a method of constructing unitary highest weight representations of the Virasoro algebra, introduced by Peter Goddard, Adrian Kent and David Olive (1986). The construction produces the complete discrete series of highest weight representations of the Virasoro algebra and demonstrates their unitarity, thus establishing the classification of unitary highest weight representations.


  • P. Goddard, A. Kent and D. Olive Unitary representations of the Virasoro and super-Virasoro algebras Comm. Math. Phys. 103, no. 1 (1986), 105–119.
  • Victor Kac (2001) [1994], "Virasoro algebra", in Hazewinkel, Michiel (ed.), Encyclopedia of Mathematics, Springer Science+Business Media B.V. / Kluwer Academic Publishers, ISBN 978-1-55608-010-4
  • V. G. Kac, A. K. Raina, Bombay lectures on highest weight representations, World Sci. (1987) ISBN 9971-5-0395-6
  • Antony Wassermann, Lecture Notes on the Kac-Moody and Virasoro algebras