The left-to-right minima basis of the group algebra of the symmetric group (updated version)
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908818939576320 |
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| author | Grinberg, Darij Vassilieva, Ekaterina A. |
| author_facet | Grinberg, Darij Vassilieva, Ekaterina A. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_02952 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The left-to-right minima basis of the group algebra of the symmetric group (updated version) Grinberg, Darij Vassilieva, Ekaterina A. Combinatorics Rings and Algebras 05A05, 16T30 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. |
| title | The left-to-right minima basis of the group algebra of the symmetric group (updated version) |
| topic | Combinatorics Rings and Algebras 05A05, 16T30 |
| url | https://arxiv.org/abs/2601.02952 |