Orbital variety closures and the convolution product in Borel-Moore homology

Vladimir Hinich, Anthony Joseph

Research output: Contribution to journalReview articlepeer-review


This paper settles a twenty-year-old conjecture describing the inclusion relations between orbital variety closures. The solution is in terms of the top Borel-Moore homology of the Steinberg variety and mirrors the way in which the Verma module multiplicities determine the inclusion relations of primitive ideals. It thus gives a link between geometry and representation theory which is more precise than what one would obtain by a naive application of the orbit method. Unlike the primitive ideal case which uses Duflo involutions, the geometric result exploits a link between correspondences and the moment map pertaining to the cotangent bundle on the flag variety. Krull equidimensionality is needed to ensure that all correspondences are recovered from the homology convolution product.

Original languageEnglish
Pages (from-to)9-36
Number of pages28
JournalSelecta Mathematica, New Series
Issue number1
StatePublished - Mar 2005

Bibliographical note

Funding Information:
Work supported in part by European Community RTN network “Liegrits” Grant No. CT-2003-5-5-78.


  • Borel-More homology
  • Orbital varieties

ASJC Scopus subject areas

  • General Mathematics
  • General Physics and Astronomy


Dive into the research topics of 'Orbital variety closures and the convolution product in Borel-Moore homology'. Together they form a unique fingerprint.

Cite this