engleski

Computing the constant term in Harish-Chandra's limit formula

Let G be a real form of a complex semisimple Lie group. We shall discuss some applications of the theory of characteristic cycles of equivariant sheaves, developed by Schmid and Vilonen, to the problems of harmonic analysis on the Lie algebra of G. The main focus will be on the classical formula of Harish-Chandra that relates the delta function supported at zero and Liouville measures on regular semisimple orbits. Such a formula is usually stated with unspecified constant term. We use the fixed point formula for the characteristic cycle of a standard sheaf associated to an open G-orbit on the flag variety to compute the constant in Harish-Chandra’s limit formula.

semisimple Lie group; flag variety; equivariant sheaf; Liouville measure

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