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arXiv · 2601.02952

The left-to-right minima basis of the group algebra of the symmetric group (updated version)

Darij Grinberg·Ekaterina A. Vassilieva
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Abstract

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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Darij Grinberg, Ekaterina A. Vassilieva. 2026-02-07. The left-to-right minima basis of the group algebra of the symmetric group (updated version). https://arxiv.org/abs/2601.02952

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