Simple modules for the partition algebra and monotone convergence of   Kronecker coefficients
  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. 
C. Bowman and M. De Visscher and J. Enyang
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