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A new descent algebra $\sum_{W}(A_{n})$ of Weyl groups of type $A_n$,constructed by present authors in [1], is generated by equivalence classes$[x_J]$ arising from the equivalence relation defined on the set of all $x_J$.In this paper, we introduce the structure of this new descent algebra forstandard parabolic subgroups $W_J$ of Weyl groups of type $A_n$.

A New Descent Algebra for Standard Parabolic Subgroups of $W(A_n)$