Geodesic
Casimir Operators on Pseudodifferential Operators of Several Variables
Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 483-493

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Zbl   EuDML

We study the actions of the Lie algebra nsl(2, C) of SL(2, C)n and the associated Casimir operator on the space of pseudodifferential operators of n variables, C denoting the complex numbers. We describe the effect of the Casimir operator on a pseudodifferential operator in connection with the symbol map and construct an nsl(2, C)-invariant lifting of the symbol map.
Classification : 11F60, 17B15, 47G30 
M. H. Lee. Casimir Operators on Pseudodifferential Operators of Several Variables. Journal of Lie Theory, Tome 12 (2002) no. 2, pp. 483-493. http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a9/
@article{JOLT_2002_12_2_a9,
     author = {M. H. Lee},
     title = {Casimir {Operators} on {Pseudodifferential} {Operators} of {Several} {Variables}},
     journal = {Journal of Lie Theory},
     pages = {483--493},
     year = {2002},
     volume = {12},
     number = {2},
     zbl = {1062.11025},
     url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_2_a9/}
}
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