JournalsrlmVol. 25, No. 3pp. 331–344

On special covariants in the exterior algebra of a simple Lie algebra

  • Corrado De Concini

    Università di Roma La Sapienza, Italy
  • Pierluigi Möseneder Frajria

    Politecnico di Milano, Campus Como, Italy
  • Paolo Papi

    Università di Roma La Sapienza, Italy
  • Claudio Procesi

    Università di Roma La Sapienza, Italy
On special covariants in the exterior algebra of a simple Lie algebra cover

Abstract

We study the subspace of the exterior algebra of a simple complex Lie algebra linearly spanned by the copies of the little adjoint representation or, in the case of the Lie algebra of traceless matrices, by the copies of the nn-th symmetric power of the defining representation. As main result we prove that this subspace is a free module over the subalgebra of the exterior algebra generated by all primitive invariants except the one of highest degree.

Cite this article

Corrado De Concini, Pierluigi Möseneder Frajria, Paolo Papi, Claudio Procesi, On special covariants in the exterior algebra of a simple Lie algebra. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), no. 3, pp. 331–344

DOI 10.4171/RLM/682