Tensor Fields of Mixed Young Symmetry Type¶and N-Complexes

@article{DuboisViolette2002TensorFO,
  title={Tensor Fields of Mixed Young Symmetry Type¶and N-Complexes},
  author={Michel Dubois-Violette and M Henneaux},
  journal={Communications in Mathematical Physics},
  year={2002},
  volume={226},
  pages={393-418}
}
Abstract: We construct N-complexes of non-completely antisymmetric irreducible tensor fields on ℝD which generalize the usual complex (N=2) of differential forms. Although, for N≥ 3, the generalized cohomology of these N-complexes is nontrivial, we prove a generalization of the Poincaré lemma. To that end we use a technique reminiscent of the Green ansatz for parastatistics. Several results which appeared in various contexts are shown to be particular cases of this generalized Poincaré lemma… 
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