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Let me introduce some background of cut and join equation for spin Hurwitz number with the completed cycle as mentioned in https://arxiv.org/pdf/1103.3120.pdf We fix two partition $\mu $ and $\nu$ of ...

We use the notation from semi-infinite wedge formalism $\bigwedge^{\infty/2}V$ with vector space $V$ generated by $$\left\{\underline{s}\mid s \in \mathbb{Z}+\frac12\right\}$$, we consider the charge ...

In Macdonald's book, the Jack symmetric function $J_{\lambda}(x_1,\ldots, x_n)$ for a partition $\lambda$ is defined by three properties (orthogonality, triangularity, and normalization). In the ...