Generalized Stability of Heisenberg Coefficients

TL;DR

This paper extends the concept of stability from Kronecker and Littlewood--Richardson coefficients to Heisenberg coefficients, classifying stable triples and exploring their generation via matrix additivity.

Contribution

It generalizes stability results to Heisenberg coefficients and classifies all stable triples, connecting previous stability notions with a new broader framework.

Findings

Stable triples for Kronecker and Littlewood--Richardson coefficients also stabilize Heisenberg coefficients.

Complete classification of triples stabilizing Heisenberg coefficients.

Use of matrix additivity to generate stable triples.

Abstract

Stembridge introduced the notion of stability for Kronecker triples which generalize Murnaghan's classical stability result for Kronecker coefficients. Sam and Snowden proved a conjecture of Stembridge concerning stable Kronecker triple, and they also showed an analogous result for Littlewood--Richardson coefficients. Heisenberg coefficients are Schur structure constants of the Heisenberg product which generalize both Littlewood--Richardson coefficients and Kronecker coefficients. We show that any stable triple for Kronecker coefficients or Littlewood--Richardson coefficients also stabilizes Heisenberg coefficients, and we classify the triples stabilizing Heisenberg coefficients. We also follow Vallejo's idea of using matrix additivity to generate Heisenberg stable triples.