engleski

Nilpotent orbital integrals

Some applications of the theory of characterictic cycles of equivariant sheaves on the flag variety, developed by Schmid and Vilonen, to the problems of the harmonic analysis on a real reductive Lie algebra will be discussed. The main focus will be on the computation of the Liouville measure on a nilpotent orbit in terms of the Liouville measures on regular semisimple orbits. A classical example of such a formula is Harish-Chandra’ s limit formula for the delta function supported at zero. A generalization of this formula to an arbitrary nilpotent orbit was the subject of study in the papers of Barbasch, Barbasch-Vogan, Hotta-Kashiwara and Rossmann. The problem was completely solved only for real rank-one groups and complex groups.

Nilpotent orbital integrals; Fourier transformation; invariant distributions; equivariant sheaves.

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