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SUMMARY:Rowena Paget (University of Kent)
DTSTART:20230110T073000Z
DTEND:20230110T083000Z
DTSTAMP:20260423T021229Z
UID:OISTRTS/46
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OISTRTS/46/"
 >Plethysm and the Partition Algebra</a>\nby Rowena Paget (University of Ke
 nt) as part of OIST representation theory seminar\n\n\nAbstract\nThe symme
 tric group $S_{mn}$ acts naturally on the collection of set partitions of 
 a set of size mn into n sets each of size m.  The irreducible constituents
  of the associated ordinary character are largely unknown\; in particular\
 , they are the subject of the longstanding Foulkes Conjecture. There are e
 quivalent reformulations using polynomial representations of infinite gene
 ral linear groups or using plethysms of symmetric functions.   I will revi
 ew plethysm from these three perspectives before presenting a new approach
  to studying plethysm: using the Schur-Weyl duality between the symmetric 
 group and the partition algebra. This method allows us to study stability 
 properties of certain plethysm coefficients. This is joint work with Chris
  Bowman. If time permits\, I will also discuss some new results with Chris
  Bowman and Mark Wildon.\n
LOCATION:https://researchseminars.org/talk/OISTRTS/46/
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