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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.

References

Goddard, P.; Kent, A.; Olive, D. (1986). "Unitary representations of the Virasoro and super-Virasoro algebras". Comm. Math. Phys. 103 (1): 105–119. Bibcode:1986CMaPh.103..105G. doi:10.1007/BF01464283. S2CID 91181508.
Victor Kac (2001) [1994], "Virasoro algebra", Encyclopedia of Mathematics, EMS Press
Kac, V. G.; Raina, A. K. (1987). Bombay lectures on highest weight representations. World Sci. ISBN 9971-5-0395-6.
Wassermann, Antony. "Lecture Notes on the Kac-Moody and Virasoro algebras". Archived from the original on 2007-03-22.

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+{{Short description|Construction for Virasoro algebras}}
-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.
+In [[mathematics]], the '''coset construction''' (or '''GKO construction''') is a method of constructing unitary [[highest weight representation]]s of the [[Virasoro algebra]], introduced by [[Peter Goddard (physicist)|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.
 ==References==
-*P. Goddard, A. Kent and D. Olive [http://projecteuclid.org/Dienst/UI/1.0/Summarize/euclid.cmp/1104114626 ''Unitary representations of the Virasoro and super-Virasoro algebras''] Comm. Math. Phys.  103, no. 1 (1986), 105–119.
+*{{cite journal |first1=P. |last1=Goddard |first2=A. |last2=Kent |first3=D. |last3=Olive |title=Unitary representations of the Virasoro and super-Virasoro algebras |journal=Comm. Math. Phys. |volume=103 |issue=1 |year=1986 |pages=105–119 |doi=10.1007/BF01464283 |bibcode=1986CMaPh.103..105G |s2cid=91181508 |url=http://projecteuclid.org/euclid.cmp/1104114626 }}
-* {{springer|author=Victor Kac|title=Virasoro algebra|id=v/v096710}}
+* {{springer|author=Victor Kac|title=Virasoro algebra|id=Virasoro_algebra}}
-*V.G. Kac,   A.K. Raina,   ''Bombay lectures on highest weight representations'', World Sci.  (1987) ISBN 9971503956
+*{{cite book |first1=V. G. |last1=Kac |first2=A. K. |last2=Raina |title=Bombay lectures on highest weight representations |publisher=World Sci.  |year=1987 |isbn=9971-5-0395-6}}
-*A. J. Wassermann, [http://iml.univ-mrs.fr/~wasserm/ Lecture Notes on the Kac-Moody and Virasoro algebras]
+*{{cite web |author1-link=Antony Wassermann |first1=Antony |last1=Wassermann |url=http://iml.univ-mrs.fr/~wasserm/ |title=Lecture Notes on the Kac-Moody and Virasoro algebras|archive-url=https://web.archive.org/web/20070322074425/http://iml.univ-mrs.fr/~wasserm/ |archive-date=2007-03-22 }}
 [[Category:Conformal field theory]]
 [[Category:Lie algebras]]
+{{quantum-stub}}