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.
On special covariants in the exterior algebra of a simple Lie algebra / DE CONCINI, Corrado; P., Möseneder Frajria; Papi, Paolo; Procesi, Claudio. - In: ATTI DELLA ACCADEMIA NAZIONALE DEI LINCEI. RENDICONTI LINCEI. MATEMATICA E APPLICAZIONI. - ISSN 1120-6330. - STAMPA. - 25:3(2014), pp. 331-344. [10.4171/RLM/682]
On special covariants in the exterior algebra of a simple Lie algebra
DE CONCINI, Corrado;PAPI, Paolo;PROCESI, Claudio
2014
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 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
