Strange Expectations in Affine Weyl Groups

Abstract

Our main result is a generalization, to all affine Weyl groups, of P. Johnson's proof of D. Armstrong's conjecture for the expected number of boxes in a simultaneous core. This extends earlier results by the second and third authors in simply-laced type. We do this by modifying and refining the appropriate notion of the "size" of a simultaneous core. In addition, we provide combinatorial core-like models for the coroot lattices in classical type and type $G_2$.