On the Enright functor in the highest weight category.
Limit formulas for groups with one conjugacy class of Cartan subgroups
Limit formulas for the computation of the canonical measure on a nilpotent coadjoint orbit in terms of the canonical measures on regular semisimple coadjoint orbits arise naturally in the study of invariant eigendistributions on a reductive Lie algebra. In the present paper we consider a particular type of the limit formula for canonical measures which was proposed by Rossmann. The main technical tool in our analysis are the results of Schmid and Vilonen on the equivariant sheaves on the flag variety...
Constant term in Harish-Chandra’s limit formula
Let be a real form of a complex semisimple Lie group . Recall that Rossmann defined a Weyl group action on Lagrangian cycles supported on the conormal bundle of the flag variety of . We compute the signed average of the Weyl group action on the characteristic cycle of the standard sheaf associated to an open -orbit on the flag variety. This result is applied to find the value of the constant term in Harish-Chandra’s limit formula for the delta function at zero.
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