English

Cartan matrices and Brauer's k(B)-Conjecture V

Representation Theory 2019-11-26 v1

Abstract

We prove Brauer's k(B)-Conjecture for the 3-blocks with abelian defect groups of rank at most 5 and for all 3-blocks of defect at most 4. For this purpose we develop a computer algorithm to construct isotypies based on a method of Usami and Puig. This leads further to some previously unknown perfect isometries for the 5-blocks of defect 2. We also investigate basic sets which are compatible under the action of the inertial group.

Keywords

Cite

@article{arxiv.1911.10710,
  title  = {Cartan matrices and Brauer's k(B)-Conjecture V},
  author = {Cesare G. Ardito and Benjamin Sambale},
  journal= {arXiv preprint arXiv:1911.10710},
  year   = {2019}
}

Comments

26 pages, 4 tables, many matrices :-)