The left-to-right minima basis of the group algebra of the symmetric group

Darij Grinberg; Ekaterina A Vassilieva

doi:10.48550/arxiv.2601.02952

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The left-to-right minima basis of the group algebra of the symmetric group

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The left-to-right minima basis of the group algebra of the symmetric group

Darij Grinberg and Ekaterina A Vassilieva

ArXiv.org

06 Jan 2026

DOI: https://doi.org/10.48550/arxiv.2601.02952

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Abstract

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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Title: The left-to-right minima basis of the group algebra of the symmetric group
Creators: Darij Grinberg - Drexel University, Mathematics
Ekaterina A Vassilieva - École Polytechnique
Publication Details: ArXiv.org
Number of pages: 21
Resource Type: Preprint
Language: English
Academic Unit: Mathematics
Other Identifier: 991022152238604721

The left-to-right minima basis of the group algebra of the symmetric group

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