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Journal of Lie Theory 12 (2002), No. 2, 483--493
Copyright Heldermann Verlag 2002

Casimir Operators on Pseudodifferential Operators of Several Variables

Min Ho Lee
Dept. of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614, U.S.A.

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.

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