The cohomology of the cotangent bundle of Heisenberg groups

Leandro Cagliero, Paulo Tirao*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Given a parabolic subalgebra g1 × n of a semisimple Lie algebra, Kostant (Ann. Math. 1963) and Griffiths (Acta Math. 1963) independently computed the g1 invariants in the cohomology group of n with exterior adjoint coefficients. By a theorem of Bott (Ann. Math. 1957), this is the cohomology of the associated compact homogeneous space with coefficients in the sheaf of local holomorphic forms. In this paper we determine explicitly the full module structure, over the symplectic group, of the cohomology group of the Heisenberg Lie algebra with exterior adjoint coefficients. This is the cohomology of the cotangent bundle of the Heisenberg group.

Original languageEnglish
Pages (from-to)276-307
Number of pages32
JournalAdvances in Mathematics
Issue number2
StatePublished - 30 Jan 2004
Externally publishedYes


  • Heisenberg Lie algebras
  • Heisenberg cotangent bundle
  • Lie cohomology
  • Sheaves cohomology


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