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.
Bibliographical noteFunding Information:
The authors are grateful for the financial support received from the Royal Commission for the
Exhibition of 1851 and EPSRC grant EP/L01078X/1.
© The Author(s) 2017.