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SUMMARY:Last steps in a proof of the McKay Conjecture on character degrees
  - Britta Späth (Bergische Universität Wuppertal)
DTSTART:20220726T104000Z
DTEND:20220726T111000Z
UID:TALK176546@talks.cam.ac.uk
DESCRIPTION:The talk will give an overview of what could be the endgame in
  the proof of McKay conjecture on character degrees. In 1972 McKay conject
 ured that for any prime p and any finite group G the set of irreducible ch
 aracters of degree prime to p has the same cardinality in G and in the nor
 malizer of its Sylow p-subgroup. The conjecture was reduced by Isaacs\, Ma
 lle and Navarro in 2007 to a stronger statement about finite quasi-simple 
 groups. Using the classification of the latter\, this focused the effort o
 n representations of finite groups of Lie type and in particular the deter
 mination of Irr(G) as an Out(G)-set for quasi-simple groups G and their p-
 local subgroups. Lusztig's parametrization of characters of overgroups G' 
 corresponding to reductive groups with connected center being the main sou
 rce of information\, quasi-simple groups of type different from D were set
 tled thanks to a mix of techniques including Shintani descent and generali
 zed Gelfand-Graev representations. I will show how adding Harish Chandra t
 heory to the picture should help settle the case of groups of type D.
LOCATION:Seminar Room 1\, Newton Institute
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