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Generalized cohomology for irreducible tensor fields of mixed Young symmetry type

Michel Dubois-Violette·Marc Henneaux
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Abstract

We construct N-complexes of non completely antisymmetric irreducible tensor fields on $\mathbb R^D$ generalizing thereby the usual complex (N=2) of differential forms. These complexes arise naturally in the description of higher spin gauge fields. Although, for $N\geq 3$, the generalized cohomology of these N-complexes is non trivial, we prove a generalization of the Poincaré lemma. Several results which appeared in various contexts are shown to be particular cases of this generalized Poincaré lemma.

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BibTeXRIS

Michel Dubois-Violette, Marc Henneaux. 1999-07-22. Generalized cohomology for irreducible tensor fields of mixed Young symmetry type. https://arxiv.org/abs/math/9907135

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