Lie Elements and Knuth Relations

@article{Schocker2002LieEA,
  title={Lie Elements and Knuth Relations},
  author={Manfred Schocker},
  journal={Canadian Journal of Mathematics},
  year={2002},
  volume={56},
  pages={871 - 882}
}
  • M. Schocker
  • Published 24 September 2002
  • Mathematics
  • Canadian Journal of Mathematics
Abstract A coplactic class in the symmetric group ${{\mathcal{S}}_{n}}$ consists of all permutations in ${{\mathcal{S}}_{n}}$ with a given Schensted $Q$ -symbol, and may be described in terms of local relations introduced by Knuth. Any Lie element in the group algebra of ${{\mathcal{S}}_{n}}$ which is constant on coplactic classes is already constant on descent classes. As a consequence, the intersection of the Lie convolution algebra introduced by Patras and Reutenauer and the coplactic… 
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