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SUMMARY:On plethysms and Sylow branching coefficients - Stacey  Law (Unive
 rsity of Cambridge)
DTSTART:20220512T102000Z
DTEND:20220512T105000Z
UID:TALK172814@talks.cam.ac.uk
DESCRIPTION:We give a recursive formula for plethysm coefficients involved
  in Foulkes&rsquo\; Conjecture\, a long-standing open problem lying at the
  intersection of the theory of symmetric functions\, the representation th
 eory of symmetric groups and algebraic combinatorics. From this we deduce 
 a stability result and resolve two conjectures of de Boeck concerning plet
 hysms. We also obtain new results on Sylow branching coefficients for symm
 etric groups for the prime 2\, the divisibility properties of which were r
 ecently used to characterise whether a Sylow subgroup of a finite group is
  normal and confirm a prediction of Malle and Navarro. This is joint work 
 with Y. Okitani.
LOCATION:Seminar Room 1\, Newton Institute
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