W∞ and the Racah-Wigner algebra

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

doi:10.1016/0550-3213(90)90539-p

Cited by 271 publications

(316 citation statements)

References 14 publications

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“…For hs(so N ) and hs λ (sl 2 ) the bilinear forms have been obtained respectively in [68] and [14]. Let us remark as well that the structure constants of hs(so 5 ) and hs λ (sl 2 ) have been proposed respectively in [5] and [15][16][17]. Actually, in the case of hs(sp 2N ), the algebraic structure is already explicit at the level of ⋆ product since there is no quotienting process to perform.…”

Section: Jhep05(2014)103mentioning

confidence: 99%

“…The precise expression for such product is quite lengthy and we refer to [15][16][17]. Instead, we show how this ⋆ product can be obtained in a relatively simple form from the bilinear and trilinear forms (3.39), (3.42).…”

Section: Jhep05(2014)103mentioning

confidence: 99%

“…It is important to note that this HS algebra is also isomorphic to the conformal HS symmetries of the free massless scalar in D − 1 dimensions [10,11]. Three-dimensional case is special: there is one-parameter family of HS algebras hs[λ] [12][13][14][15][16][17] corresponding to the one-parameter family of backgrounds of the 3D interacting equations [18,19]. 1 Besides the explicit construction through oscillators, the aforementioned HS algebras can be also obtained as a quotient of universal enveloping algebra (UEA) of the isometry algebra.…”

Section: Jhep05(2014)103mentioning

confidence: 99%

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Notes on higher-spin algebras: minimal representations and structure constants

Joung

Mkrtchyan

2014

J. High Energ. Phys.

148

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The higher-spin (HS) algebras relevant to Vasiliev's equations in various dimensions can be interpreted as the symmetries of the minimal representation of the isometry algebra. After discussing this connection briefly, we generalize this concept to any classical Lie algebra and consider the corresponding HS algebras. For sp 2N and so N , the minimal representations are unique so we get unique HS algebras. For sl N , the minimal representation has one-parameter family, so does the corresponding HS algebra. The so N HS algebra is what underlies the Vasiliev theory while the sl 2 one coincides with the 3D HS algebra hs [λ]. Finally, we derive the explicit expression of the structure constant of these algebras -more precisely, their bilinear and trilinear forms. Several consistency checks are carried out for our results.

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Section: Jhep05(2014)103mentioning

confidence: 99%

Section: Jhep05(2014)103mentioning

confidence: 99%

Section: Jhep05(2014)103mentioning

confidence: 99%

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Notes on higher-spin algebras: minimal representations and structure constants

Joung

Mkrtchyan

2014

J. High Energ. Phys.

148

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“…with some constants g k,s,ℓ n,m , C k,s n ∈ C. For example, the standard basis for the W 1+∞ generators [13] is…”

Section: The Free Boson Fieldmentioning

confidence: 99%

“…The W 1+∞ algebra 3.1. The W 1+∞ algebra with central charge c = 1 [13] is nothing but the algebra of "local" bilinears of fermions; the generating currents…”

Section: The Free Boson Fieldmentioning

confidence: 99%

Eigensystem and full character formula of theW 1+? algebra withc = 1

Awata¹,

Fukuma²,

Одаке³

et al. 1994

Lett Math Phys

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Metaplectic Covariance of the Weyl–Wigner–Groenewold–Moyal Quantization and Beyond

Verçin

1998

Annals of Physics

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The metaplectic covariance for all forms of the Weyl-Wigner-GroenewoldMoyal quantization is established with different realizations of the inhomogeneous symplectic algebra. Beyond that, in its most general form W ∞ -covariance of this quantization scheme is investigated, and explicit expressions for the quantum-deformed Hamiltonian vector fields are presented. In a general basis the structure constants of the W ∞ -algebra are obtained and its subalgebras are analyzed.

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W∞ and the Racah-Wigner algebra

Cited by 271 publications

References 14 publications

Notes on higher-spin algebras: minimal representations and structure constants

Notes on higher-spin algebras: minimal representations and structure constants

Eigensystem and full character formula of theW 1+? algebra withc = 1

Metaplectic Covariance of the Weyl–Wigner–Groenewold–Moyal Quantization and Beyond

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