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

被引：5
|
作者：
De Concini, Corrado [1 ]
Frajria, Pierluigi Moesneder [2 ]
Papi, Paolo [1 ]
Procesi, Claudio [1 ]
机构：
[1] Univ Roma La Sapienza, Dipartimento Matemat, I-00185 Rome, Italy
[2] Politecn Milan, Polo Reg Como, I-22100 Como, Italy
来源：
RENDICONTI LINCEI-MATEMATICA E APPLICAZIONI | 2014年 / 25卷 / 03期
关键词：
Exterior algebra; invariants; little adjoint representation; small representation; THEOREM;
D O I：
10.4171/RLM/682
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
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页码：331 / 344
页数：14
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