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SUMMARY:Characters of odd degree of symmetric groups - Eugenio Giannelli
DTSTART:20170201T163000Z
DTEND:20170201T173000Z
UID:TALK70390@talks.cam.ac.uk
CONTACT:Christopher Brookes
DESCRIPTION:Let G be a finite group and let P be a Sylow p-subgroup of G. 
 Denote by\nIrr_{p'}(G) the set consisting of all irreducible characters of
  G of degree\ncoprime to p.\nThe McKay Conjecture asserts that |Irr_{p'}(G
 )|=|Irr_{p'}(N_G(P))|.\nSometimes\, we do not only have the above equality
 \, but it is also possible\nto determine explicit natural bijections (McKa
 y bijections) between\nIrr_{p'}(G) and Irr_{p'}(N_G(P)).\nIn the first par
 t of this talk I will describe a recently obtained natural\nMcKay bijectio
 n for symmetric groups S_n at the prime p=2.\nIn the second part of the ta
 lk I will present a recent joint work with A.\nKleshchev\, G. Navarro and 
 P.H. Tiep\, concerning the construction of natural\nbijections between Irr
 _{p'}(G) and Irr_{p'}(H) for various classes of finite\ngroups G and corre
 sponding subgroups H of odd index.\n
LOCATION:MR12
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