-Whittaker vectors for complex semisimple Lie groups, wave front sets, and Goldie rank polynomial representations
Let be a real form of a complex semisimple Lie group . Recall that Rossmann defined a Weyl group action on Lagrangian cycles supported on the conormal bundle of the flag variety of . We compute the signed average of the Weyl group action on the characteristic cycle of the standard sheaf associated to an open -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.