Geometry Seminar
Date: October 25, 2019
Time: 4:00PM - 5:00PM
Location: BLOC 628
Speaker: Jordyn Harriger, Indiana University
Title: Planar Algebras Related to the Symmetric Groups.
Abstract: What makes the symmetric groups special ? Well, one interesting thing about S_n is that it has a subgroup of index n and that the permutation representation of S_n comes from inducing the trivial representation of that subgroup. How could this generalize if n was not an integer? Using planar algebras we can describe Rep(S_n) graphically. Then using this graphical description we can construct a planar algebra for Rep(S_t), where t is not an integer, via inter- polation between the Rep(S_n)'s. Additionally, I will describe how this planar algebra can from a special biadjunction between tensor categories, which gen- eralizes the induction and restriction relations between S_n and S_{n-1}. I will also discuss the relationship between these planar algebras and usual partition algebra description of Rep(S_t).