Spin representations of symmetric groups in characteristic 2

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• Matthew Fayers, Queen Mary University of London
• Wednesday 31 January 2024, 16:30-17:30
• MR12.

If you have a question about this talk, please contact Adam Jones.

Let G be a finite group and p a prime. Then there is a well-defined (at the level of characters) process of p-modular reduction for representations of G. It sometimes happens that two different ordinary irreducible characters can become the same when reduced modulo p, and it is interesting to determine exactly when this happens. For example, if G is the symmetric group, and two ordinary irreducibles are obtained from each other by tensoring with the sign representation, then their reductions modulo 2 will be the same.

In this talk we consider this problem for the double covers of the symmetric groups in characteristic 2; in fact, we solve the more general problem of when the 2-modular reductions of two characters are proportional to each other. I will give the result, and explain some of the techniques used to prove it.

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

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