Journal of Lie Theory
Vol. 12, No. 2, pp. 483--493 (2002)
Casimir operators on pseudodifferential operators of several variables
Min Ho LeeMin Ho Lee
Department of Mathematics
University of Northern Iowa
Cedar Falls, Iowa 50614
Abstract: We study the actions of the Lie algebra $n\slf (2,\Bbb C)$ of $SL(2, \Bbb C)^n$ and the associated Casimir operator on the space of pseudodifferential operators of $n$ variables. We describe the effect of the Casimir operator on a pseudodifferential operator in connection with the symbol map and construct an $n\slf (2,\Bbb C)$-invariant lifting of the symbol map.
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Electronic fulltext finalized on: 6 May 2002. This page was last modified: 21 May 2002.