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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Last steps in a proof of the McKay Conjecture on c
haracter degrees - Britta Späth (Bergische Univers
ität Wuppertal)
DTSTART;TZID=Europe/London:20220726T114000
DTEND;TZID=Europe/London:20220726T121000
UID:TALK176546AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/176546
DESCRIPTION:The talk will give an overview of what could be th
e endgame in the proof of McKay conjecture on char
acter degrees. In 1972 McKay conjectured that for
any prime p and any finite group G the set of irre
ducible characters of degree prime to p has the sa
me cardinality in G and in the normalizer of its S
ylow p-subgroup. The conjecture was reduced by Isa
acs\, Malle and Navarro in 2007 to a stronger stat
ement about finite quasi-simple groups. Using the
classification of the latter\, this focused the ef
fort on representations of finite groups of Lie ty
pe and in particular the determination of Irr(G) a
s an Out(G)-set for quasi-simple groups G and thei
r p-local subgroups. Lusztig's parametrization of
characters of overgroups G' corresponding to reduc
tive groups with connected center being the main s
ource of information\, quasi-simple groups of type
different from D were settled thanks to a mix of
techniques including Shintani descent and generali
zed Gelfand-Graev representations. I will show how
adding Harish Chandra theory to the picture shoul
d help settle the case of groups of type D.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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