The lattice permutation condition for Kronecker tableaux (Extended Abstract)

TL;DR

This paper extends the lattice permutation condition to Kronecker tableaux, enabling the calculation of new stable Kronecker coefficients, and identifies families where combinatorics simplifies significantly.

Contribution

It generalizes the lattice permutation condition to Kronecker tableaux and simplifies combinatorics for specific co-Pieri triples.

Findings

Calculation of a large new class of stable Kronecker coefficients

Identification of families with simplified combinatorics

Extension of lattice permutation condition to Kronecker tableaux

Abstract

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.