Zobrazeno 1 - 10
of 175
pro vyhledávání: '"Natanzon S"'
Publikováno v:
Lett.Math.Phys. 111 (2021) 124
We present a review of the spin Hurwitz numbers, which count the ramified coverings with spin structures. They are related to peculiar $Q$ Schur functions, which are actually related to characters of the Sergeev group. This allows one to put the whol
Externí odkaz:
http://arxiv.org/abs/2012.09847
Autor:
Natanzon, S. M., Orlov, A. Yu.
We consider integrals of tau functions of Zakharov-Shabat systems whose higher times are related to the eigenvalues of products of random matrices. Apart of random matrices there is the set of $n$ pairs of given matrices which play the role of parame
Externí odkaz:
http://arxiv.org/abs/1911.02003
Publikováno v:
Eur. Phys. J. C 80 (2020) 97
Spin Hurwitz numbers are related to characters of the Sergeev group, which are the expansion coefficients of the Q Schur functions, depending on odd times and on a subset of all Young diagrams. These characters involve two dual subsets: the odd parti
Externí odkaz:
http://arxiv.org/abs/1904.11458
Autor:
Natanzon, S., Zabrodin, A.
We find all formal solutions to the $\hbar$-dependent KP hierarchy. They are characterized by certain Cauchy-like data. The solutions are found in the form of formal series for the tau-function of the hierarchy and for its logarithm (the F-function).
Externí odkaz:
http://arxiv.org/abs/1509.04472
Autor:
Natanzon, S. M., Orlov, A. Yu.
We consider special series in ratios of the Schur functions which are defined by integers $\textsc{f}\ge 0$ and $\textsc{e} \le 2$, and also by the set of $3k$ parameters $n_i,q_i,t_i,\,i=1,..., k$. These series may be presented in form of matrix int
Externí odkaz:
http://arxiv.org/abs/1407.8323
Publikováno v:
JHEP 11 (2014) 080
There is now a renewed interest to the Hurwitz tau-function, counting the isomorphism classes of Belyi pairs, arising in the study of equilateral triangulations and Grothiendicks's dessins d'enfant. It is distinguished by belonging to a particular fa
Externí odkaz:
http://arxiv.org/abs/1405.1395
Autor:
Natanzon, S. M., Zabrodin, A. V.
We explicitly construct the series expansion for a certain class of solutions to the 2D Toda hierarchy in the zero dispersion limit, which we call symmetric solutions. We express the Taylor coefficients through some universal combinatorial constants
Externí odkaz:
http://arxiv.org/abs/1302.7288
Publikováno v:
Journal of Knot Theory and Its Ramifications Vol. 23, No. 7 (2014) 1450033
The classical Hurwitz numbers of degree n together with the Hurwitz numbers of the seamed surfaces of degree n give rise to the Klein topological field theory. We extend this construction to the Hurwitz numbers of all degrees at once. The correspondi
Externí odkaz:
http://arxiv.org/abs/1212.2041
Publikováno v:
Journal of Geometry and Physics, 73 (2013) 243-251
Motivated by the algebraic open-closed string models, we introduce and discuss an infinite-dimensional counterpart of the open-closed Hurwitz theory describing branching coverings generated both by the compact oriented surfaces and by the foam surfac
Externí odkaz:
http://arxiv.org/abs/1210.6955