**
Jacob
Campbell,
Department
of
Pure
Mathematics,
University
of
Waterloo**

This is the first meeting of a learning seminar which will run for most of July and August. The proposed day/time for the seminar is on Fridays, 2:30 to 3:30 pm.

In the first few meetings of the seminar we will look at the representation theory of the finite symmetric groups S_n, following the approach of Okounkov and Vershik, which emphasizes the branching rule and the use of Jucys-Murphy elements (all these terms are to be explained as the seminar goes on).

We will then move to the infinite symmetric group S_{\infty}, which requires making some modifications to the notion of a character, in order to account for infinite-dimensional representations. This part of the learning seminar will be directed towards the classical theorem of Thoma which parameterizes the extremal characters of S_{\infty}.

References

[1] Representation theory of the symmetric groups, by T. Ceccherini-Silberstein, F. Scarabotti and F. Tolli, Cambridge University Press, 2010.

[2] Representations of the infinite symmetric group, by A. Borodin and G. Olshanski, Cambridge University Press, 2017.