Characters of odd degree of symmetric groups

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• Eugenio Gianelli, University of Cambridge
• Wednesday 25 January 2017, 15:00-16:00
• Watson Building, Lecture Room B.

If you have a question about this talk, please contact David Craven.

LMS Groups and their applications triangle meeting

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 prime 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 the construction of McKay bijections for symmetric groups at the prime p=2.

In the second part of the talk I will present a recent joint work with Kleshchev, Navarro and 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 includes the case G=S_n and H any maximal subgroup of odd index in S_n, as well as the construction of McKay bijections for solvable and general linear groups.

This talk is part of the Algebra seminar series.

This talk is included in these lists:

• Algebra seminar
• School of Mathematics events
• Watson Building, Lecture Room B

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