Lie Elements and Knuth Relations
Rings and Algebras
2007-05-23 v1 Combinatorics
Abstract
A coplactic class in the symmetric group S_n consists of all permutations in 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 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 algebra introduced by Poirier and Reutenauer is the Solomon descent algebra.
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Cite
@article{arxiv.math/0209327,
title = {Lie Elements and Knuth Relations},
author = {Manfred Schocker},
journal= {arXiv preprint arXiv:math/0209327},
year = {2007}
}
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15 pages