Stability and ribbon bases for the rank-selected homology of geometric lattices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910210699821056 |
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| author | Hersh, Patricia Sundaram, Sheila |
| author_facet | Hersh, Patricia Sundaram, Sheila |
| contents | This paper analyzes the representation theoretic stability, in the sense of Thomas Church and Benson Farb, of the rank-selected homology of the Boolean lattice and the partition lattice, proving sharp uniform representation stability bounds in both cases. It proves a conjecture of the first author and Reiner by giving the sharp stability bound for general rank sets for the partition lattice. Along the way, a new homology basis sharing useful features with the polytabloid basis for Specht modules is introduced for the rank-selected homology and for the rank-selected Whitney homology of any geometric lattice, resolving an old open question of Björner. These bases give a matroid theoretic analogue of Specht modules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_06479 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Stability and ribbon bases for the rank-selected homology of geometric lattices Hersh, Patricia Sundaram, Sheila Combinatorics Algebraic Topology Representation Theory 05E18, 05E45, 05B35, 05E10, 20C30, 05A18, 05A07, 55U15 This paper analyzes the representation theoretic stability, in the sense of Thomas Church and Benson Farb, of the rank-selected homology of the Boolean lattice and the partition lattice, proving sharp uniform representation stability bounds in both cases. It proves a conjecture of the first author and Reiner by giving the sharp stability bound for general rank sets for the partition lattice. Along the way, a new homology basis sharing useful features with the polytabloid basis for Specht modules is introduced for the rank-selected homology and for the rank-selected Whitney homology of any geometric lattice, resolving an old open question of Björner. These bases give a matroid theoretic analogue of Specht modules. |
| title | Stability and ribbon bases for the rank-selected homology of geometric lattices |
| topic | Combinatorics Algebraic Topology Representation Theory 05E18, 05E45, 05B35, 05E10, 20C30, 05A18, 05A07, 55U15 |
| url | https://arxiv.org/abs/2604.06479 |