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On the Action of Galois Automorphisms on Characters and Navarro's Sylow 2-Normalizer Conjectures

Connections for Women: Group Representation Theory and Applications February 01, 2018 - February 02, 2018

February 01, 2018 (03:30 PM PST - 04:15 PM PST)
Speaker(s): Amanda Schaeffer Fry (Metropolitan State University of Denver)
Location: MSRI: Simons Auditorium
Tags/Keywords
  • Local-global conjectures

  • characters

  • McKay Conjecture

  • self-normalizing Sylow subgroups

  • fi nite simple groups

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC
Video

4-Fry

Abstract

Navarro has conjectured a necessary and sufficient condition for a finite group G to have a self-normalizing Sylow 2-subgroup, which is given in terms of the behavior of the ordinary irreducible characters of G under a specific Galois automorphism. Navarro-Tiep-Vallejo have conjectured a similar statement regarding groups whose Sylow 2-normalizers contain a single irreducible 2-Brauer character. Thanks to reduction theorems proved by myself and Navarro-Vallejo, respectively, a large part of the proofs of these conjectures is to understand the action of this Galois automorphism on characters of groups of Lie type. I will discuss the recent proof of these conjectures, including a description of the action of Galois automorphisms on characters of groups of Lie type

Supplements
30632?type=thumb 2018.02.01.0330.Schaeffer-Fry 298 KB application/pdf Download
Video/Audio Files

4-Fry

H.264 Video 4-Fry.mp4 305 MB video/mp4 rtsp://videos.msri.org/data/000/030/528/original/4-Fry.mp4 Download
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