Minimal heights and defect groups with two character degrees
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910317326368768 |
|---|---|
| author | Malle, Gunter Moretó, Alexander Rizo, Noelia |
| author_facet | Malle, Gunter Moretó, Alexander Rizo, Noelia |
| contents | Conjecture A of \cite{EM14} predicts the equality between the smallest positive height of the irreducible characters in a $p$-block of a finite group and the smallest positive height of the irreducible characters in its defect group. Hence, it can be seen as a generalization of Brauer's famous height zero conjecture. One inequality was shown to be a consequence of Dade's Projective Conjecture. We prove the other, less well understood, inequality for principal blocks when the defect group has two character degrees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19816 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Minimal heights and defect groups with two character degrees Malle, Gunter Moretó, Alexander Rizo, Noelia Representation Theory Group Theory Conjecture A of \cite{EM14} predicts the equality between the smallest positive height of the irreducible characters in a $p$-block of a finite group and the smallest positive height of the irreducible characters in its defect group. Hence, it can be seen as a generalization of Brauer's famous height zero conjecture. One inequality was shown to be a consequence of Dade's Projective Conjecture. We prove the other, less well understood, inequality for principal blocks when the defect group has two character degrees. |
| title | Minimal heights and defect groups with two character degrees |
| topic | Representation Theory Group Theory |
| url | https://arxiv.org/abs/2305.19816 |