Lie Elements and Knuth Relations

[摘要] A coplactic class in the symmetric group $Sym_n$ consists of allpermutations in $Sym_n$ with a given Schensted $Q$-symbol, and maybe described in terms of local relations introduced by Knuth. AnyLie element in the group algebra of $Sym_n$ which is constant oncoplactic classes is already constant on descent classes. As aconsequence, the intersection of the Lie convolution algebraintroduced by Patras and Reutenauer and the coplactic algebraintroduced by Poirier and Reutenauer is the direct sum of allSolomon descent algebras.

[学科分类] 数学（综合）