Conformally invariant differential operators on tensor densities

Details Conformally invariant differential operators on tensor densities Conformally invariant differential operators on tensor densities

2001-04-25

arxiv.org/abs/math/0104232v1

Mathematics

Differential Geometry

11 pages, LaTeX

Scientific paper

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.

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