Logo image
New search Researchers Research units
Sign in
The left-to-right minima basis of the group algebra of the symmetric group (updated version)
Preprint

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

Darij Grinberg and Ekaterina A Vassilieva
ArXiv.org
06 Jan 2026

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.

Metrics

1 Record Views

Details

Logo image