Configuration spaces and peak representations
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915444655390720 |
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| author | Aguiar, Marcelo Brauner, Sarah Reiner, Victor |
| author_facet | Aguiar, Marcelo Brauner, Sarah Reiner, Victor |
| contents | Within the group algebras of the symmetric and hyperoctahedral groups, one has their descent algebras and families of Eulerian idempotents. These idempotents are known to generate group representations with topological interpretations, as the cohomology of configuration spaces of types A and B. We provide an analogous cohomological interpretation for the representations generated by idempotents in the peak algebra, called the peak representations. We describe the peak representations as sums of Thrall's higher Lie characters, give Hilbert series and branching rule recursions for them, and discuss a connection to Jordan brackets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_09898 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Configuration spaces and peak representations Aguiar, Marcelo Brauner, Sarah Reiner, Victor Combinatorics Representation Theory 05E10, 14N20, 52C35, 55R80 Within the group algebras of the symmetric and hyperoctahedral groups, one has their descent algebras and families of Eulerian idempotents. These idempotents are known to generate group representations with topological interpretations, as the cohomology of configuration spaces of types A and B. We provide an analogous cohomological interpretation for the representations generated by idempotents in the peak algebra, called the peak representations. We describe the peak representations as sums of Thrall's higher Lie characters, give Hilbert series and branching rule recursions for them, and discuss a connection to Jordan brackets. |
| title | Configuration spaces and peak representations |
| topic | Combinatorics Representation Theory 05E10, 14N20, 52C35, 55R80 |
| url | https://arxiv.org/abs/2508.09898 |