A new higher-spin algebra and the lone-star product

Pope, C.N.; Romans, L.J.; Shen, Xianfeng

doi:10.1016/0370-2693(90)91782-7

Cited by 134 publications

(83 citation statements)

References 5 publications

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“…Indeed, we could have introduced a parameter q in the realisation, corresponding to the one occurring in refs. [7,8,10,11 ], which would give W~ when q¢0 and woo when q = 0. The lower-order terms in (27) would all be multiplied by powers of q, and thus will disappear when q is set to zero.…”

Section: ~= K~y 1+ ' Oy -(L+ 1 ) Klylox mentioning

confidence: 99%

“…=g(fl~ = -k0+flt + (l+ 1 )flt0+k) + 6(?t = fit 0_ k), [6(k), c~(7't) ] =6(7; = (l+2)7t0+ k-kO+ ~'t) • (10) In order to have a gauged realisation ofwo~ in which the higher gauge fields play a more essential role, it is necessary to consider a multi-component model, e.g. with fg=SU(N), or SL(N, g~).…”

Section: The Chiral Woo Theorymentioning

confidence: 99%

“…Here too, the algebra may be enlarged to W~ +oo, by the addition of generators with conformal spin 1 [ 8,10 ]. The W~ +o~ algebra may be realised as the algebra of all smooth differential operators (of arbitrary degree) on the circle [ 11 ], and this provides us with a convenient starting point for a coset construction.…”

Section: ~= K~y 1+ ' Oy -(L+ 1 ) Klylox mentioning

confidence: 99%

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W∞ gravity

et al. 1990

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We construct a gauge theory of woo gravity coupled to scalars. For scalar fields valued in some-finite-dimensional Lie algebra, a complete realisation of gauged w~ can be given using a number of gauge fields equal to the rank of the Lie algebra. We show how the theory can be truncated to describe a gauge theory of Ws gravity, and we give the explicit result for W3. We show that the transformations of the scalar fields can be interpreted as a non-linear realisation on the coset w~ +oo/w~.

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Section: ~= K~y 1+ ' Oy -(L+ 1 ) Klylox mentioning

confidence: 99%

Section: The Chiral Woo Theorymentioning

confidence: 99%

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W∞ gravity

et al. 1990

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“…and the variations 27) determine, after long but straightforward computation, the fixed time t 0 Dirac bracket algebra (3.14) by means of (2.12). 8 The .…”

Section: Jhep03(2015)081mentioning

confidence: 99%

“…The element V 1 0 denotes the identity operator. To define the algebra we use the -product representation constructed in [27]: where we remind the reader that by (δ . .…”

Section: A Conventionsmentioning

confidence: 99%

About the phase space of SL(3) black holes

Cabo-Bizet

Giraldo-Rivera

2015

J. High Energ. Phys.

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In this note we address some issues of recent interest, related to the asymptotic symmetry algebra of higher spin black holes in sl(3, R) × sl(3, R) Chern Simons (CS) formulation. We compute the fixed time Dirac bracket algebra that acts on two different phase spaces. Both of these spaces contain black holes as zero modes. The result for one of these phase spaces is explicitly shown to be isomorphic to W

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Quasifinite Representations of Classical Lie Subalgebras of 1+∞

Kač¹,

Wang²,

Yan³

1998

Advances in Mathematics

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We show that there are precisely two, up to conjugation, anti-involutions _ \ of the algebra of differential operators on the circle preserving the principal gradation. We classify the irreducible quasifinite highest weight representations of the central extension D \ of the Lie subalgebra of this algebra fixed by &_ \ , and find the unitary ones. We realize them in terms of highest weight representations of the central extension of the Lie algebra of infinite matrices with finitely many non-zero diagonals over the algebra C[u]Â(u m+1 ) and its classical Lie subalgebras of B, C and D types. Character formulas for positive primitive representations of D \ (including all the unitary ones) are obtained. We also realize a class of primitive representations of D \ in terms of free fields and establish a number of duality results between these primitive representations and finite-dimensional irreducible representations of finitedimensional Lie groups and supergroups. We show that the vacuum module V c of D + carries a vertex algebra structure and establish a relationship between V c for c # 1 2 Z and W-algebras. Academic Press

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A new higher-spin algebra and the lone-star product

Cited by 134 publications

References 5 publications

W∞ gravity

W∞ gravity

About the phase space of SL(3) black holes

Quasifinite Representations of Classical Lie Subalgebras of 1+∞

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