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SUMMARY:The diameter of the modular McKay graph of SLn(Fp). - Miriam Norri
 s\, King's College London
DTSTART:20220211T150000Z
DTEND:20220211T160000Z
UID:TALK169325@talks.cam.ac.uk
CONTACT:Tom Adams
DESCRIPTION:*Zoom Details:\nJoin Zoom Meeting\nhttps://zoom.us/j/951856627
 80?pwd=Y3FZTTBNMG1NZEtyNEhQMHJBdCtvZz09\n\nMeeting ID: 951 8566 2780\nPass
 code: 040109*\n\nFor G a finite group\, F an algebraically closed field an
 d W a faithful FG-module the McKay graph\, MF (G\, W)\, is a connected dir
 ected graph on the set of simple FG-modules. There is an edge in the graph
  from V1 to V2 if V2 occurs as a composition factor of V1 ⊗ W . These gr
 aphs famously come up in the McKay correspondence which says that such gra
 phs for finite subgroups of SU2(C) will be affine Dynkin diagrams of type 
 A\, D or E. \n\nIn the case where the characteristic of F divides the orde
 r of G\, finding the composition factors of tensor products is a very hard
  problem. However it might surprise you to know that taking G to be SLn(Fp
 )\, F the algebraic closure of Fp and W the standard n-dimensional FSLn(Fp
 )-module we can show\n\ndiam MF(G\,W)= ½(p−1)(n2 −n).\n\nIn this talk
  I will describe these graphs in a bit more detail\, give some background 
 and explain how we are able to prove this neat formula for the diameter wi
 thout explicitly constructing the graphs. 
LOCATION:Zoom
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