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Characters of odd degree of symmetric groups

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  • UserEugenio Giannelli
  • ClockWednesday 01 February 2017, 16:30-17:30
  • HouseMR12.

If you have a question about this talk, please contact Christopher Brookes.

Let G be a finite group and let P be a Sylow p-subgroup of G. Denote by Irr_{p’}(G) the set consisting of all irreducible characters of G of degree coprime to p. The McKay Conjecture asserts that |Irr_{p’}(G)|=|Irr_{p’}(N_G(P))|. Sometimes, we do not only have the above equality, but it is also possible to determine explicit natural bijections (McKay bijections) between Irr_{p’}(G) and Irr_{p’}(N_G(P)). In the first part of this talk I will describe a recently obtained natural McKay bijection for symmetric groups S_n at the prime p=2. In the second part of the talk I will present a recent joint work with A. Kleshchev, G. Navarro and P.H. Tiep, concerning the construction of natural bijections between Irr_{p’}(G) and Irr_{p’}(H) for various classes of finite groups G and corresponding subgroups H of odd index.

This talk is part of the Algebra and Representation Theory Seminar series.

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