A New Descent Algebra of Weyl Groups of Type An
  In this paper we define an equivalence relation on the set of all $x_{J}$ in order to form a basis for a new descent algebra of Weyl groups of type $A_{n}$. By means of this, we construct a new commutative and semi-simple descent algebra of Weyl groups of type $A_{n}$ generated by equivalence classes arising from this equivalence relation. 
Tulay Yagmur, Himmet Can
math.AC math.RT