Abstract
Symplectic Q-functions are a symplectic analogue of Schur Q-functions and defined as the t=−1 specialization of Hall–Littlewood functions associated with the root system of type C. In this paper we prove that symplectic Q-functions share many of the properties of Schur Q-functions, such as a tableau description and a Pieri-type rule. And we present some positivity conjectures, including the positivity conjecture of structure constants for symplectic P-functions. We conclude by giving a tableau description of factorial symplectic Q-functions.
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