A Hodge Decomposition for the Complex of Injective

  title={A Hodge Decomposition for the Complex of Injective},
  author={P. D. Hanlon and Patricia Hersh},
Reiner and Webb (preprint, 2002) compute the Sn-module structure for the complex of injective words. This paper refines their formula by providing a Hodge type decomposition. Along the way, this paper proves that the simplicial boundary map interacts in a nice fashion with the Eulerian idempotents. The Laplacian acting on the top chain group in the complex of injective words is also shown to equal the signed random to random shuffle operator. Uyemura-Reyes, 2002, conjectured that the (unsigned… CONTINUE READING

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