English

Defect of characters of the symmetric group

Representation Theory 2013-01-09 v1

Abstract

Following the work of B. Kuelshammer, J. B. Olsson and G. R. Robinson on generalized blocks of the symmetric groups, we give a definition for the \ell-defect of characters of the symmetric group S_n, where \ell > 1 is an arbitrary integer. We prove that the \ell -defect is given by an analogue of the hook-length formula, and use it to prove, when n < \ell^2, an \ell-version of the McKay Conjecture in S_n .

Keywords

Cite

@article{arxiv.0902.2349,
  title  = {Defect of characters of the symmetric group},
  author = {Jean-Baptiste Gramain},
  journal= {arXiv preprint arXiv:0902.2349},
  year   = {2013}
}

Comments

To appear in Journal of Group Theory, 10 pages