Mathematics - Combinatorics Mathematics - Rings and Algebras
We introduce a new basis of the group algebra of the symmetric group, built using the left-to-right minima sets of permutations. We show that on this basis, the descent algebra acts by triangular operators, thus making it an analogue of a cellular basis. The proof involves Dynkin elements (nested commutators) of the free algebra and their interactions with the$\mathbf B$ -basis.
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The left-to-right minima basis of the group algebra of the symmetric group