2023/09/25 by Eric Nathan Stucky, Stucky, Eric Nathan, Marko Thiel +3
Mathematics · #Advanced Combinatorial Mathematics #Random Matrices and Applications #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2309.14481
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 G2.