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arXiv · 1810.12512

Generalized Stability of Heisenberg Coefficients

Li Ying
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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.

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Li Ying. 2018-10-30. Generalized Stability of Heisenberg Coefficients. https://arxiv.org/abs/1810.12512

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