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Abstract
摘要 |
We present an explicit fermionic representation of the Kontsevich-Witten (KW) τ -function, and establish a relationship to the Hurwitz partition function by a GL(∞) group operator. Then, from the Virasoro constraint of the Kontsevich matrix model, we get the Virasoro constraint for the Hurwitz partition function, and the Virasoro constraint completely determines the Schur polynomials representation of the Hurwitz partition function. For a Generalised Kontsevich Matrix model (GKMM), we express the partition function in terms of the Schur polynomials. While for certain given potential, it is a r-reduced KP τ -function, and then the r-spin intersection numbers are obtained.
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