Schur Q-Polynomials and Kontsevich–Witten Tau Function
Xiaobo Liu , Chenglang Yang
Peking Mathematical Journal ›› 2023, Vol. 7 ›› Issue (2) : 713 -758.
Schur Q-Polynomials and Kontsevich–Witten Tau Function
Using matrix model, Mironov and Morozov recently gave a formula which represents Kontsevich–Witten tau function as a linear expansion of Schur Q-polynomials. In this paper, we will show directly that the Q-polynomial expansion in this formula satisfies the Virasoro constraints, and consequently obtains a proof of this formula without using matrix model. We also give a proof for Alexandrov’s conjecture that Kontsevich–Witten tau function is a hypergeometric tau function of the BKP hierarchy after re-scaling.
National Natural Science Foundation of China(11890662)
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