Séminaire Lotharingien de Combinatoire, B80d (2019), 26 pp.

Emmanuel Briand, Peter R. W. McNamara, Rosa Orellana and Mercedes Rosas

Commutation and Normal Ordering for Operators on Symmetric Functions

Abstract. We study the commutation relations and normal ordering between families of operators on symmetric functions. These operators can be naturally defined by the operations of multiplication, Kronecker product, and their adjoints. As applications, we give a new proof of the skew Littlewood-Richardson rule and prove an identity about the Kronecker product with a skew Schur function.

Received: June 4, 2018. Revised: April 14, 2019. Accepted: April 14, 2019.

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