Séminaire Lotharingien de Combinatoire, 80B.42 (2018), 12 pp.

Li Ying

Stability of the Heisenberg Product on Symmetric Functions

Abstract. The Heisenberg product is an associative product defined on symmetric functions which interpolates between the usual product and the Kronecker product. 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. We also show a rectangular symmetry for the Schur structural constants of this product.

Received: November 14, 2017. Accepted: February 17, 2018. Final version: April 1, 2018.

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