Limit formulas for groups with one conjugacy class of Cartan subgroups
Copyright policy )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 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 Lie groups with one conjugacy class of Cartan subgroups.
limit formula, Semisimple Lie groups and their representations, Analysis on real and complex Lie groups, Analysis on other specific Lie groups, nilpotent orbit; Liouville measure; Weyl group; limit formula, Weyl group, nilpotent orbit, Liouville measure
limit formula, Semisimple Lie groups and their representations, Analysis on real and complex Lie groups, Analysis on other specific Lie groups, nilpotent orbit; Liouville measure; Weyl group; limit formula, Weyl group, nilpotent orbit, Liouville measure
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