Computational bounds for doing harmonic analysis on permutation modules of finite groups (Mike Orrison, HMC)

In this talk, I will describe an approach to finding upper bounds for the number of arithmetic operations necessary for doing harmonic analysis on permutation modules of finite groups. The approach takes advantage of the intrinsic orbital structure of permutation modules, and it uses the multiplicities of irreducible submodules within individual orbital spaces to express the resulting computational bounds. I will then conclude by showing that these bounds are surprisingly small when dealing with certain permutation modules arising from the action of the symmetric group on tabloids. This is joint work with Michael Hansen, Masanori Koyama, Matthew McDermott, and Sarah Wolff.