## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

Friday, July 12, 2019 — 2:30 PM EDT

**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.

University of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x33484

Fax: 519 725 0160

Email: puremath@uwaterloo.ca

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1