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Spherical harmonics on superspace

Kevin Coulembier
Torsdag, 10 maj, 2012, at 16:15, in Aud. D4 (1531-219)
We introduce Riemannian geometry on flat superspace. The null solutions of the Laplace operator are called harmonic functions. We characterize the harmonic polynomials as a representation of the orthosymplectic Lie superalgebra. This algebra generalizes the algebra of infinitesimal rotations to superspace. The harmonic polynomials also constitute a representation of the super conformal algebra. This generalizes the minimal representation of the orthogonal algebra and the corresponding ideal in the universal enveloping algebra is of Joseph type.
Kontaktperson: Bent Ørsted