engleski

Constant term in Harish-Chandra's limit formula

Let $G_\mathbb{;R};$ be a real form of a complex semisimple Lie group $G$. Recall that Rossmann defined a Weyl group action on Lagrangian cycles supported on the conormal bundle of the flag variety of $G$. We compute the signed average of the Weyl group action on the characteristic cycle of the standard sheaf associated to an open $G_\mathbb{;R};$-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.

flag variety; equivariant sheaf; characteristic cycle; coadjoint orbit; Liouville measure

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