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CHARACTERISTIC CYCLES OF STANDARD SHEAVES ASSOCIATED WITH OPEN ORBITS

By Communicated Dan Barbasch

Abstract

Abstract. Let GR be a real form of a complex, semisimple Lie group G. We compute the characteristic cycle of a standard sheaf associated with an open GR-orbit on the partial flag variety of G. We apply the result to obtain a Rossmann-type integral formula for elliptic coadjoint orbits. These results were previously obtained by the author under the assumption that the rank of GR is equal to the rank of a maximal compact subgroup. Let GR be a linear, semisimple Lie group. The present paper is a complement to [1], where we obtained a limit formula for elliptic orbital integrals. The proof of the formula was based on the powerful theory of characteristic cycles of equivariant sheaves developed by Schmid and Vilonen in [2], [3] and [4]. An important ingredient in the argument was the formula for the characteristic cycle of a standard sheaf on a generalized flag variety associated to an open GR-orbit, which was proved under the assumption that the rank of GR is equal to the rank of a maximal compact subgroup. The goal of this paper is to extend the formula for the characteristic cycle to the case of nonequal ranks. Compared to the proof of the correspondin

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.3221
Provided by: CiteSeerX
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