Sl ( 2 , R ) - Module Structure of the Eigenspaces of the Casimir Operator
نویسندگان
چکیده
In this paper, on the space of smooth sections of a SL(2, R)-homogeneous vector bundle. over the upper half plane we study the SL(2, R) structure for the eigenspaces of the Cru;;imir operator. That is, we determine its Jordan-Holder' sequence and the sode filttation. We compute a suitable generalized principal series having as a quotient a giver} eigenspace. We also give an integral equation which characterizes the elements of a given eigenspace. Finally, we study the eigenspaces of twisted Dirac operators. §
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