engleski

Limit formulas for groups with one conjugacy class of Cartan subgroups

Limit formulas for the computation 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 and their characteristic cycles. We combine the theory of Schmid and Vilonen and the work of Rossmann to compute canonical measures on nilpotent orbits for the real semisimple groups with one conjugacy class of Cartan subgroups.

nilpotent orbit; Liouville measure; Weyl group; limit formula

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