Descent algebra

From Wikipedia, the free encyclopedia
Jump to navigation Jump to search

In algebra, Solomon's descent algebra of a Coxeter group is a subalgebra of the integral group ring of the Coxeter group, introduced by Solomon (1976).

The descent algebra of the symmetric group

In the special case of the symmetric group Sn, the descent algebra is given by the elements of the group ring such that permutations with the same descent set have the same coefficients. (The descent set of a permutation σ consists of the indices i such that σ(i) > σ(i+1).) The descent algebra of the symmetric group Sn has dimension 2n-1. It contains the peak algebra as a left ideal.


Retrieved from ""
This content was retrieved from Wikipedia :
This page is based on the copyrighted Wikipedia article "Descent algebra"; it is used under the Creative Commons Attribution-ShareAlike 3.0 Unported License (CC-BY-SA). You may redistribute it, verbatim or modified, providing that you comply with the terms of the CC-BY-SA