RECORD
The Character Triple Conjecture for maximal defect characters and the prime 2
Representation Theory · Submitted 25 Jul 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We prove that Sp\"ath's Character Triple Conjecture holds for every finite group with respect to maximal defect characters at the prime 2.
The compiled record
The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
Open the compiled record
The abstract, sentence by sentence
We prove that Sp\"ath's Character Triple Conjecture holds for every finite group with respect to maximal defect characters at the prime 2. This is done by reducing the maximal defect case of the conjecture to the so-called inductive Alperin-McKay condition whose verification has recently been completed by Ruhstorfer for the prime 2. As a consequence we obtain the Character Triple Conjecture for all 2-blocks with abelian defect groups by applying Brauer's Height Zero Conjecture, a proof of which is now available. We also obtain similar results for the block-free version of the Character Triple Conjecture at any prime p.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We prove that Sp\"ath's Character Triple Conjecture holds for every finite group with respect to maximal defect characters at the prime 2. | result 0.90 | 0.96 | 0.97 | asserted 1.00 |
| s1 | This is done by reducing the maximal defect case of the conjecture to the so-called inductive Alperin-McKay condition whose verification has recently been completed by Ruhstorfer for the prime 2. | method 0.99 | 0.81 | 0.06 | asserted 1.00 |
| s2 | As a consequence we obtain the Character Triple Conjecture for all 2-blocks with abelian defect groups by applying Brauer's Height Zero Conjecture, a proof of which is now available. | result 0.87 | 0.79 | 0.09 | asserted 1.00 |
| s3 | We also obtain similar results for the block-free version of the Character Triple Conjecture at any prime p. | result 0.98 | 0.90 | 0.06 | asserted 1.00 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
The paper
Original abstract
We prove that Sp\"ath's Character Triple Conjecture holds for every finite group with respect to maximal defect characters at the prime 2. This is done by reducing the maximal defect case of the conjecture to the so-called inductive Alperin-McKay condition whose verification has recently been completed by Ruhstorfer for the prime 2. As a consequence we obtain the Character Triple Conjecture for all 2-blocks with abelian defect groups by applying Brauer's Height Zero Conjecture, a proof of which is now available. We also obtain similar results for the block-free version of the Character Triple Conjecture at any prime p.
Human review
How the literature uses it
1 arXiv paper cite this in 1 sentence
Papers citing it
Cites it as background 1 paper
-
For what concerns the validity of the Character Triple Conjecture, we mention that it has been verified in [ref] for all finite groups with respect to maximal defect characters and the prime $2$ (using Ruhstorfer's results from [ref] ) while the study of the conjecture for groups of Lie type in non-defining characteristic has been initiated by the author following ideas of Broué, Fong, and Srinivasan (see the series of papers [ref] , [ref] , [ref] , and [ref] ).
A reduction theorem for the Character Triple Conjecture · Introduction · 0.85
What it cites · 5 sentences without a confident label
Cites as background 4 papers
-
Regarding the state of the art of the Character Triple Conjecture, we refer the reader to [ref] for the case of sporadic groups, special linear groups of degree $2$, and blocks with cyclic defect, to [ref] for the case of $p$-solvable groups, and to the series of papers [ref] , [ref] , [ref] , and [ref] for the case of finite simple groups of Lie type in non-defining characteristic.
Inductive local-global conditions and generalized Harish-Chandra theory · Preliminaries and notation · 1.00
-
Regarding the state of the art of the Character Triple Conjecture, we refer the reader to [ref] for the case of sporadic groups, special linear groups of degree $2$, and blocks with cyclic defect, to [ref] for the case of $p$-solvable groups, and to the series of papers [ref] , [ref] , [ref] , and [ref] for the case of finite simple groups of Lie type in non-defining characteristic.
A local-global principle for unipotent characters · Preliminaries and notation · 1.00
-
Regarding the state of the art of the Character Triple Conjecture, we refer the reader to [ref] for the case of sporadic groups, special linear groups of degree $2$, and blocks with cyclic defect, to [ref] for the case of $p$-solvable groups, and to the series of papers [ref] , [ref] , [ref] , and [ref] for the case of finite simple groups of Lie type in non-defining characteristic.
The Brown complex in non-defining characteristic and applications · Preliminaries and notation · 1.00
Discussion
Know something about this paper? Leave a comment, or highlight any passage above to comment on it.