Stability of Heisenberg Coefficients
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The Heisenberg product is an associative product defined on symmetric functions which interpolates between the ordinary product and the Kronecker product. Heisenberg coefficients are Schur structure constants of the Heisenberg product and generalization of both Littlewood–Richardson coefficients and Kronecker coefficients. In 1938, Murnaghan discovered that the Kronecker product of two Schur functions stabilizes. We prove an analogous result for the Heisenberg product of Schur functions. In 2014, Stembridge introduced the notion of stability for Kronecker triples which generalize Murnaghan’s classical stability result. Sam and Snowden proved a conjecture of Stembridge concerning stable Kronecker triples, and they also showed an analogous result for Littlewood–Richardson 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 Manivel and Vallejo’s idea of using matrix additivity to generate Heisenberg stable triples.
Ying, Li (2019). Stability of Heisenberg Coefficients. Doctoral dissertation, Texas A&M University. Available electronically from