engleski

Stable Nilpotent Orbital Integrals

We shall discuss some applications of the theory of characteristic cycles of equivariant sheaves on the flag variety, developed by Rossmann, Schmid and Vilonen, to the problems of harmonic analysis on a real reductive Lie algebra. Our goal will be to understand the space of stably invariant distributions associated with complex nilpotent orbit. The dimension of this space was computed by Kottwitz and Assem conjectured how to obtain a natural basis. Assem’s conjecture will be examined in a number of special cases.

semisimple Lie group; flag variety; equivariant sheaves; nilpotent orbit; stable invariant distribution

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