We introduce a new symmetric function that plays the role of skew Schur function for symplectic groups. Many combinatorial identities for this function are developed and employed to construct the Symplectic Schur Process. This new probability ensemble shares many desirable properties with the classical Schur process of Okounkov-Reshetikhin and we will explain some of them in this talk, including the property of being a determinantal point process, the connection to the Berele insertion algorithm and, finally, we discuss some applications. This talk is based on joint work with Matteo Mucciconi.
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