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Pré-Publication, Document De Travail Année : 2001

Conformally invariant differential operators on tensor densities

Résumé

Let ${\cal F}_\lambda$ be the space of tensor densities on ${\bf R}^n$ of degree $\lambda$ (or, equivalently, of conformal densities of degree $-\lambda{}n$) considered as a module over the Lie algebra $so(p+1,q+1)$. We classify $so(p+1,q+1)$-invariant bilinear differential operators from ${\cal F}_\lambda\otimes{\cal F}_\mu$ to~${\cal F}_\nu$. The classification of linear $so(p+1,q+1)$-invariant differential operators from ${\cal F}_\lambda$ to ${\cal F}_\mu$ already known in the literature is obtained in a different manner.

Dates et versions

hal-00138273 , version 1 (24-03-2007)

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Citer

V. Ovsienko, P. Redou. Conformally invariant differential operators on tensor densities. 2001. ⟨hal-00138273⟩
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