Stembridge introduced the notion of stability for Kronecker triples, which generalizes Murnaghan’s classical stability result for Kronecker coefficients. Sam and Snowden proved a conjecture of Stembridge concerning stable Kronecker triples, 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.

Stembridge引入了Kronecker三元组的稳定性的概念，它推广了Murnaghan关于Kronecker系数的经典稳定性结果。Sam和Snowden证明了Stembridge关于稳定Kronecker三元组的猜想，并且他们还给出了Littlewood-Richardson系数的类似结果。Heisenberg系数是Heisenberg积的Schur结构常数，可以同时推广Littlewood–Richardson系数和Kronecker系数。我们显示，对于Kronecker系数或Littlewood-Richardson系数，任何稳定的三元组也会使Heisenberg系数稳定，并对稳定Heisenberg系数的三元组进行分类。我们还遵循Vallejo的使用矩阵可加性生成Heisenberg稳定三元组的想法。