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|Title:||Higher symmetries of the square of the Laplacian|
|Citation:||Proceedings of Symmetries and Overdetermined Systems of Partial Differential Equations, 2008 / vol.144, pp.319-338|
|Series/Report no.:||The IMA Volumes in Mathematics and its Applications ; 144|
|Conference Name:||Symmetries and Overdetermined Systems of Partial Differential Equations (17 Jul 2008 - 04 Aug 2006 : USA)|
|Michael Eastwood and Thomas Leistner|
|Abstract:||The symmetry operators for the Laplacian in flat space were recently described and here we consider the same question for the square of the Laplacian. Again, there is a close connection with conformal geometry. There are three main steps in our construction. The first is to show that the symbol of a symmetry is constrained by an overdetermined partial differential equation. The second is to show existence of symmetries with specified symbol (using a simple version of the AdS/CFT correspondence). The third is to compute the composition of two first order symmetry operators and hence determine the structure of the symmetry algebra. There are some interesting differences as compared to the corresponding results for the Laplacian.|
|Keywords:||Symmetry algebra; Laplacian; conformal geometry|
|Appears in Collections:||Mathematical Sciences publications|
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