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.

中文翻译：

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辛Q函数

辛Q函数是Schur Q函数的辛类似物，定义为$Ť=-\mathrm{1个}$与C型根系统相关的Hall–Littlewood函数的特殊化。在本文中，我们证明辛Q函数具有Schur Q函数的许多特性，例如画面描述和Pieri型规则。并且我们提出了一些正猜想，包括关于辛P函数的结构常数的正猜想。我们通过给出阶乘辛Q函数的表格描述来结束。