Oliver Ruff (University of Sydney)
Friday 21st April, 12.05-12.55pm, Carslaw 159
Weight theory for alternating groups
This talk is about the ordinary representation theory of the alternating group. We use the general strategy introduced by Okounkov and Vershik in their work on the symmetric group, which makes it necessary to introduce analogues of the Young-Jucys-Murphy elements. The "weights" of the title are joint eigenvalues of these elements. Analysis of the weights enables us to classify and construct the simple modules in a natural way, and also provides an elementary representation-theoretic explanation of the branching rule.
If time permits, we will discuss the extent to which this generalizes to the modular theory.