Simple modules for the partition algebra and monotone convergence of Kronecker coefficients

C. Bowman, M. De Visscher, J. Enyang

Published 2016-07-28Version 1

We construct bases of the simple modules for partition algebras which are indexed by paths in an alcove geometry. This allows us to give a concrete interpretation (and new proof) of the monotone convergence property for Kronecker coefficients using stratifications of the cell modules of the partition algebra.