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- W2100642214 abstract "The spaces of linear differential operators on ${mathbb{R}}^n$ acting on tensor densities of degree $lambda$ and the space of functions on $T^*{mathbb{R}}^n$ which are polynomial on the fibers are not isomorphic as modules over the Lie algebra $Vect({mathbb{R}}^n)$ of vector fields on ${mathbb{R}}^n$. However, these modules are isomorphic as $sl(n+1,{mathbb{R}})$-modules where $sl(n+1,{mathbb{R}})subset Vect({mathbb{R}}^n)$ is the Lie algebra of infinitesimal projective transformations. In addition, such an $sl_{n+1}$-equivariant bijection is unique (up to normalization). This leads to a notion of projectively equivariant quantization and symbol calculus for a manifold endowed with a (flat) projective structure. We apply the $sl_{n+1}$-equivariant symbol map to study the $Vect(M)$-modules of linear differential operators acting on tensor densities, for an arbitrary manifold $M$." @default.
- W2100642214 created "2016-06-24" @default.
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- W2100642214 date "1998-09-11" @default.
- W2100642214 modified "2023-10-18" @default.
- W2100642214 title "Projectively equivariant symbol calculus" @default.
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