## Contact Info

Pure MathematicsUniversity of Waterloo

200 University Avenue West

Waterloo, Ontario, Canada

N2L 3G1

Departmental office: MC 5304

Phone: 519 888 4567 x43484

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 x43484

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

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is centralized within our Office of Indigenous Relations.