Preprint
The left-to-right minima basis of the group algebra of the symmetric group (updated version)
ArXiv.org
06 Jan 2026
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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Details
- Title
- The left-to-right minima basis of the group algebra of the symmetric group (updated version)
- Creators
- Darij GrinbergEkaterina A Vassilieva
- Publication Details
- ArXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991022152238604721