Invariant generalized functions supported on an orbit

Avraham Aizenbud; Dmitry Gourevitch

doi:10.1007/s11856-018-1668-2

Invariant generalized functions supported on an orbit

Department of Mathematics

Weizmann Institute of Science

Research output: Contribution to journal › Article › peer-review

Abstract

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 GL(3)(C). Our main tool is the notion of generalized functions on a real algebraic stack, introduced recently in [Sak16].

Original language	English GB
Pages (from-to)	411-426
Number of pages	16
Journal	Israel Journal of Mathematics
Volume	225
Issue number	1
DOIs	https://doi.org/10.1007/s11856-018-1668-2
State	Published - Apr 2018

ASJC Scopus subject areas

General Mathematics

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10.1007/s11856-018-1668-2

http://arxiv.org/abs/1701.00411License: Other

Cite this

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abstract = "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 GL(3)(C). Our main tool is the notion of generalized functions on a real algebraic stack, introduced recently in [Sak16].",

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AB - 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 GL(3)(C). Our main tool is the notion of generalized functions on a real algebraic stack, introduced recently in [Sak16].

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DO - 10.1007/s11856-018-1668-2

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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

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Invariant generalized functions supported on an orbit

Abstract

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