The left-to-right minima basis of the group algebra of the symmetric group (updated version)
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.
Fields of Study & Subjects
Advanced Combinatorial Mathematics
Finite Group Theory Research
Advanced Operator Algebra Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 6 January 2026
- Document type
- Preprint