Israel Journal of Mathematics

, Volume 225, Issue 1, pp 411–426 | Cite as

Invariant generalized functions supported on an orbit

  • Avraham Aizenbud
  • Dmitry Gourevitch


We study the space of invariant generalized functions supported on an orbit of the action of a real algebraic group on a real algebraic manifold. This space is equipped with the Bruhat filtration. We study the generating function of the dimensions of the filtras, and give some methods to compute it. To illustrate our methods we compute those generating functions for the adjoint action of GL3(C). Our main tool is the notion of generalized functions on a real algebraic stack, introduced recently in [Sak16].


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© Hebrew University of Jerusalem 2018

Authors and Affiliations

  1. 1.Faculty of Mathematics and Computer ScienceWeizmann Institute of ScienceRehovotIsrael

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