2 results
Generalized Descent Algebras
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- Journal:
- Canadian Mathematical Bulletin / Volume 50 / Issue 4 / 01 December 2007
- Published online by Cambridge University Press:
- 20 November 2018, pp. 535-546
- Print publication:
- 01 December 2007
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- Article
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If
$A$ is a subset of the set of reflections of a finite Coxeter group 
$W$, we define a sub-
$\mathbb{Z}$-module 
${{\mathcal{D}}_{A}}\left( W \right)$ of the group algebra 
$\mathbb{Z}W$. We discuss cases where this submodule is a subalgebra. This family of subalgebras includes strictly the Solomon descent algebra, the group algebra and, if $W$ is of type 
$B$, the Mantaci–Reutenauer algebra.
Lie Elements and Knuth Relations
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- Journal:
- Canadian Journal of Mathematics / Volume 56 / Issue 4 / 01 August 2004
- Published online by Cambridge University Press:
- 20 November 2018, pp. 871-882
- Print publication:
- 01 August 2004
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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 algebra introduced by Poirier and Reutenauer is the direct sum of all Solomon descent algebras.
