We study cut-and-join operators for spin Hurwitz partition functions. We provide explicit expressions for these operators in terms of derivatives in p-variables without straightforward matrix realization, which is yet to be found. With the help of these expressions spin cut-and-join operators can be calculated directly and algorithmically. The reason why it is possible is the connection between mentioned operators and specially chosen Casimir operators that are easy to compute. An essential part of the connection involves shifted Q-Schur functions.

中文翻译：

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cut-and-join 和 Casimir 运算符之间的连接

我们研究了自旋 Hurwitz 分区函数的剪切和连接算子。我们根据p变量的导数为这些运算符提供了显式表达式，而没有直接的矩阵实现，这还有待发现。借助这些表达式，可以直接通过算法计算自旋切割和连接运算符。之所以可能，是因为上面提到的算子与特别选择的易于计算的 Casimir 算子之间的联系。连接的一个重要部分涉及移位 Q-Schur 函数。