University of Birmingham > Talks@bham > Birmingham and Warwick Algebra Seminar  > On the character degree sets of Sn, An and related groups

On the character degree sets of Sn, An and related groups

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

Conference: Representations of Symmetric Groups, Hecke Algebras and KLR Algebras

It is a long standing question due to Brauer to find out what the complex group algebra CG tells about the finite group G, i.e., what can be deduced on the structure of G from the multiset of degrees of its irreducible characters. Concluding the work by Nguyen and Tong-Viet on quasisimple groups, in joint work with them and Olsson, the double covers of the symmetric and alternating groups were considered. For nonabelian simple groups G, Huppert conjectured that just the character degree set (without multiplicities) determines G up to an abelian factor. For alternating groups An, this was shown by Huppert up to n=11, and by Nguyen, Tong-Viet and Wakefield for n=12,13. I will report on progress on this obtained in recent joint work with Tong-Viet and Jiping Zhang.

This talk is part of the Birmingham and Warwick Algebra Seminar series.

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