arXiv subjects
Publications and source records attributed to J. Enyang.
We recently generalised the lattice permutation condition for Young tableaux to Kronecker tableaux and hence calculated a large new class of stable Kronecker coefficients labelled by co-Pieri triples. In this extended abstract we discuss important families of co-Pieri triples for which our combinatorics simplifies drastically.
A fundamental problem in the representation theory of the symmetric group, Sn, is to describe the coefficients in the decomposition of a tensor product of two simple representations. These coefficients are known in the literature as the Kronecker coefficients. The Littlewood--Richardson coefficients appear as an important subfamily of the wider class of stable Kronecker coefficients. This subfamily of coefficients can be calculated using a tableaux counting algorithm known as the Littlewood--Richardson rule. This paper generalises one half of this rule (the "co-Pieri" rule) to the the wider family of stable 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.
We provide an explicit construction of skew cell modules for diagram algebras.