# Pieri rule for the factorial Schur $P$-functions

• ### Soojin Cho

Ajou University, Suwon, Republic of Korea
• ### Takeshi Ikeda

Okayama University of Science, Japan

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## Abstract

We prove an identity expressing the product of two factorial Schur $P$-functions as an alternating sum of the factorial Schur $P$-functions with explicitly defined coefficients depending on the deformation parameters. As an application, we derive the Pieri rule for the factorial Schur $P$-functions.