Ordering the representations of S_n using the interchange process

Inspired by Aldous' conjecture for the spectral gap of the interchange process and its recent resolution by Caputo, Liggett and Richthammer, we define an associated order on the irreducible representations of S_n. Aldous' conjecture is equivalent to certain representations being comparable in this order, and hence determining the "Aldous order" completely is a generalized question. We show a few additional entries in this order.