turkmath.org

Symmetry groups of binary trees are isomorphic to iterated wreath products of symmetric groups of order two. In our collaboration with Mee Seong Im, our aim was to describe the relations between induction and restriction on representations of this tower of groups, which embed into each other. Even though we didn't get a full description of the relevant category, we have partial results concerning the vector space and algebra structure of certain hom spaces. In the talk I will focus on the origin of the problem and various approaches we found helpful during our research.