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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:On plethysms and Sylow branching coefficients - St
acey Law (University of Cambridge)
DTSTART;TZID=Europe/London:20220512T112000
DTEND;TZID=Europe/London:20220512T115000
UID:TALK172814AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/172814
DESCRIPTION:We give a recursive formula for plethysm coefficie
nts involved in Foulkes&rsquo\; Conjecture\, a lon
g-standing open problem lying at the intersection
of the theory of symmetric functions\, the represe
ntation theory of symmetric groups and algebraic c
ombinatorics. From this we deduce a stability resu
lt and resolve two conjectures of de Boeck concern
ing plethysms. We also obtain new results on Sylow
branching coefficients for symmetric groups for t
he prime 2\, the divisibility properties of which
were recently used to characterise whether a Sylow
subgroup of a finite group is normal and confirm
a prediction of Malle and Navarro. This is joint w
ork with Y. Okitani.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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