论文信息 - The Orlik-Solomon algebra on the partition lattice and the free Lie algebra

The Orlik-Solomon algebra on the partition lattice and the free Lie algebra

Abstract In the same spirit as before, we relate the action of S n on the Orlik-Solomon algebra of the partition lattice to the action of S n on the exterior algebra of the free Lie algebra. More precisely, we construct an explicit basis in each of those spaces and then we show that the matrices of adjacent transposition in one space are equal to minus the transpose of the matrices in the other space. This equality shows that the first S n -module is the dual of the other, tensored by the sign-representation.

Nantel Bergeron | Hélène Barcelo | N. Bergeron | H. Barcelo

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