The EMS Publishing House is now EMS Press and has its new home at ems.press.

Please find all EMS Press journals and articles on the new platform.

Rendiconti Lincei - Matematica e Applicazioni


Full-Text PDF (133 KB) | Metadata | Table of Contents | RLM summary
Volume 25, Issue 3, 2014, pp. 331–344
DOI: 10.4171/RLM/682

Published online: 2014-08-31

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

Corrado De Concini[1], Pierluigi Möseneder Frajria[2], Paolo Papi[3] and Claudio Procesi[4]

(1) Università di Roma La Sapienza, Italy
(2) Politecnico di Milano, Campus Como, Italy
(3) Università di Roma La Sapienza, Italy
(4) Università di Roma La Sapienza, Italy

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 $n$-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.

Keywords: Exterior algebra, invariants, little adjoint representation, small representation

De Concini Corrado, Möseneder Frajria Pierluigi, Papi Paolo, Procesi Claudio: On special covariants in the exterior algebra of a simple Lie algebra. Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. 25 (2014), 331-344. doi: 10.4171/RLM/682