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In their recent inspiring paper Mironov and Morozov claim a surprisinglysimple expansion formula for the Kontsevich-Witten tau-function in terms of theSchur Q-functions. Here we provide a similar conjecture for theBr\'ezin-Gross-Witten tau-function. Moreover, we identify both tau-functions ofthe KdV hierarchy, which describe intersection numbers on the moduli spaces ofpunctured Riemann surfaces, with the hypergeometric solutions of the BKPhierarchy.

Intersection numbers on $\overline {\mathcal M}_{g,n}$ and BKP hierarchy