Conformally invariant differential operators on tensor densities
Conformally invariant differential operators on tensor densities
复制标题
张量密度上的共形不变微分算子
DOI：
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发表时间：
2001
期刊：
影响因子：
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通讯作者：
P. Redou
中科院分区：
文献类型：
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作者：
V. Ovsienko;P. Redou
设$(p+1，q+1)$上的张量密度空间被认为是李代数$So(p+1，q+1)上的模张量密度空间(或者等价地，是度为$-λn$的共形密度)。我们将$so(p+1，q+1)$-不变双线性微分算子从$\cal F}_\lambda\oTimes{\cal F}_\u$分类到~$\cal F}_\nu$。用另一种方法得到了文献中已知的线性$so(p+1，q+1)$不变微分算子从$\cal F}_\lambda$到${cal F}_\u$的分类。
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.