Higher symmetries of the laplacian

By Michael Eastwood. 2002

295 citations recorded by the source corpus.

We identify the symmetry algebra of the Laplacian on Euclidean space as an explicit quotient of the universal enveloping algebra of the Lie algebra of conformal motions. We construct analogues of these symmetries on a general conformal manifold.

Subfields: Algebra and Number Theory, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6a18842513072982912da8f18761b980f542bf4e

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Citations in the corpus

On conformal Killing symmetric tensor fields on Riemannian manifolds (2011, background): “Conformal Killing symmetric tensor fields of higher rank naturally appear in various problems of physics and geometry (see [21, 7, 8, 13, 20, 6, 1]).”
Maximally homogeneous para-CR manifolds of semisimple type (2006, unknown): “for example [FG85], [CSS01], [CD01], [ E05 ], [J06]).”
Nonlinear equations for symmetric massless higher spin fields in (A)dSd (2003, methodology): “Such an algebra was described recently by Eastwood in [25] as the algebra of conformal HS symmetries of the free masless Klein-Gordon equation in d−1 dimensions.”
Nonlinear higher spin theories in various dimensions (2005, methodology): “The realization of the conformal HS algebra h in any dimension in terms of a quotient of the universal enveloping algebra(10) U(o(d, 2)) was given by Eastwood in [53].”
Conformal higher spin theory (2002, background): “(12)An independent proof of this statement is in fact contained in paper [41], which has appeared when the present paper has been prepared for publication.”
On the uniqueness of higher-spin symmetries in AdS and CFT (2013, methodology): “Analogously to charges QA(s−1),B(s−1), forming an algebra as a consequence of the CFT axioms, the Vasiliev connections WA(s−1),B(s−1) are gauge fields of a higher-spin algebra [12, 17], which is at the core of the higher-spin theory of [17].”
Higher order singletons, partially massless fields and their boundary values in the ambient approach (2013, methodology): “The following lemma, which was obtained through the success iv works [5, 11, 12], is important from the present perspective because it should be interpreted as a new candidate HS algebra.”
Effective action in a higher-spin background (2010, background): “32) for d > 2 corresponds to the enveloping algebra of so(d, 2) , that is the higherspin algebra identified by Eastwood and Vasiliev [18, 34] (for d = 2, one gets two copies of the W∞ algebra with zero central charge [35]).”
AdS description of induced higher-spin gauge theory (2013, background): “As shown in [51], see also [48,49], the symmetric traceless conformal Killing tensors of rank s− 1 form an irreducible representation of SO(d+ 1, 1) of dimension”