@article {2014,
	title = {Minimal Liouville gravity correlation numbers from Douglas string equation},
	number = {Journal of high energy physics;volume 2014; issue 1; article number 156;},
	year = {2014},
	publisher = {Springer},
	abstract = {We continue the study of $(q,p)$ Minimal Liouville Gravity with the help of
Douglas string equation. We generalize the results of \cite{Moore:1991ir},
\cite{Belavin:2008kv}, where Lee-Yang series $(2,2s+1)$ was studied, to
$(3,3s+p_0)$ Minimal Liouville Gravity, where $p_0=1,2$. We demonstrate that
there exist such coordinates $\tau_{m,n}$ on the space of the perturbed Minimal
Liouville Gravity theories, in which the partition function of the theory is
determined by the Douglas string equation. The coordinates $\tau_{m,n}$ are
related in a non-linear fashion to the natural coupling constants
$\lambda_{m,n}$ of the perturbations of Minimal Lioville Gravity by the
physical operators $O_{m,n}$. We find this relation from the requirement that
the correlation numbers in Minimal Liouville Gravity must satisfy the conformal
and fusion selection rules. After fixing this relation we compute three- and
four-point correlation numbers when they are not zero. The results are in
agreement with the direct calculations in Minimal Liouville Gravity available
in the literature \cite{Goulian:1990qr}, \cite{Zamolodchikov:2005sj},
\cite{Belavin:2006ex}.},
	doi = {10.1007/JHEP01(2014)156},
	url = {http://urania.sissa.it/xmlui/handle/1963/34588},
	author = {Alexander Belavin and Boris Dubrovin and Baur Mukhametzhanov}
}
@article {2000,
	title = {Monodromy of certain Painlev{\'e}-VI transcendents and reflection groups},
	journal = {Invent. Math. 141 (2000) 55-147},
	number = {arXiv.org;math/9806056v1},
	year = {2000},
	publisher = {Springer},
	abstract = {We study the global analytic properties of the solutions of a particular family of Painleve\\\' VI equations with the parameters $\\\\beta=\\\\gamma=0$, $\\\\delta={1\\\\over2}$ and $\\\\alpha$ arbitrary. We introduce a class of solutions having critical behaviour of algebraic type, and completely compute the structure of the analytic continuation of these solutions in terms of an auxiliary reflection group in the three dimensional space. The analytic continuation is given in terms of an action of the braid group on the triples of generators of the reflection group. This result is used to classify all the algebraic solutions of our Painleve\\\' VI equation.},
	doi = {10.1007/PL00005790},
	url = {http://hdl.handle.net/1963/2882},
	author = {Boris Dubrovin and Marta Mazzocco}
}
