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Of all publications in the section: 48
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Article
Frenkel E., Feigin B. L. Communications in Mathematical Physics. 1990. Vol. 128. No. 1. P. 161-189.
Article
Braverman A., Rybnikov L. G., Feigin B. L. et al. Communications in Mathematical Physics. 2011. Vol. 308. No. 2. P. 457-478.
Recently Alday, Gaiotto and Tachikawa proposed a conjecture relating 4-dimensional super-symmetric gauge theory for a gauge group G with certain 2-dimensional conformal field theory. This conjecture implies the existence of certain structures on the (equivariant) intersection cohomology of the Uhlenbeck partial compactification of the moduli space of framed G-bundles on P^2. More precisely, it predicts the existence of an action of the corresponding W-algebra on the above cohomology, satisfying certain properties. We propose a "finite analog" of the (above corollary of the) AGT conjecture.
Article
Pugai Y., Feigin B. L., Miwa T. et al. Communications in Mathematical Physics. 1998. Vol. 191. No. 3. P. 501-541.
Article
Marshall I. Communications in Mathematical Physics. 1990. No. 133. P. 509-520.
Article
Takeyama Y., Фейгин Б. Л., Miwa T. и др. Communications in Mathematical Physics. 2005. Т. 257. № 2. С. 395-423.
Article
Marshall I. Communications in Mathematical Physics. 2015. Vol. 338. No. 2. P. 563-587.

Hamiltonian reduction is used to project a trivially integrable system on the Heisenberg double of SU(n; n), to obtain a system of Ruijsenaars type on a suitable quotient space. This system possesses BCn symmetry and is shown to be equivalent to the standard three-parameter BCn hyperbolic Sutherland model in the cotangent bundle limit.

Article
Fedotov A., Sandomirskiy F. Communications in Mathematical Physics. 2015. Vol. 334. No. 2. P. 1083-1099.

Article
Takebe T. Communications in Mathematical Physics. 1997. Vol. 183. P. 161-182.
Article
Olshanetsky M., Khesin B., Levin A. Communications in Mathematical Physics. 2004. Vol. 250. P. 581-612.
Article
M.A. Bershtein, A.I.Shchechkin. Communications in Mathematical Physics. 2015. Vol. 339. No. 3. P. 1021-1061.

In 2012, Gamayun, Iorgov, and Lisovyy conjectured an explicit expression for the Painlevé VI τ function in terms of the Liouville conformal blocks with central charge c = 1. We prove that the proposed expression satisfies Painlevé VI τ function bilinear equations (and therefore prove the conjecture). The proof reduces to the proof of bilinear relations on conformal blocks. These relations were studied using the embedding of a direct sum of two Virasoro algebras into a sum of Majorana fermion and Super Virasoro algebra. In the framework of the AGT correspondence, the bilinear equations on the conformal blocks can be interpreted in terms of instanton counting on the minimal resolution of \$\${\mathbb{C}^2/\mathbb{Z}_2}\$\$C2/Z2 (similarly to Nakajima–Yoshioka blow-up equations). © 2015, Springer-Verlag Berlin Heidelberg.

Article
Takebe T., Kuroki G. Communications in Mathematical Physics. 1999. Vol. 204. P. 587-618.
Article
Levin A., Olshanetsky M., Smirnov A. et al. Communications in Mathematical Physics. 2012. Vol. 316. No. 1. P. 1-44.
Article
Loktev S., Tipunin I., Feigin B. L. Communications in Mathematical Physics. 2002. Vol. 229. No. 2. P. 271-292.
Article
Bufetov A. I., Qiu Y. Communications in Mathematical Physics. 2017. Vol. 351. No. 1. P. 1-44.

We study determinantal point processes on D induced by the reproducing kernels of generalized Bergman spaces. In the first case, we show that all reduced Palm measures of the same order are equivalent. The Radon–Nikodym derivatives are computed explicitly using regularized multiplicative functionals. We also show that these determinantal point processes are rigid in the sense of Ghosh and Peres, hence reduced Palm measures of different orders are singular. In the second case, we show that all reduced Palm measures, of all orders, are equivalent. The Radon–Nikodym derivatives are computed using regularized multiplicative functionals associated with certain Blaschke products. The quasi-invariance of these determinantal point processes under the group of diffeomorphisms with compact supports follows as a corollary.

Article
Olshanetsky M., Levin A. Communications in Mathematical Physics. 1997. Vol. 188. P. 449-466.
Article
Frenkel E., Feigin B. L. Communications in Mathematical Physics. 1991. Vol. 137. No. 3. P. 617-639.
Article
Marshall I., Feher L. Communications in Mathematical Physics. 1997. No. 183. P. 423-461.
Article
Gavrylenko P., Lisovyy O. Communications in Mathematical Physics. 2018. Vol. 363. No. 1. P. 1-58.

We derive Fredholm determinant representation for isomonodromic tau functions of Fuchsian systems with n regular singular points on the Riemann sphere and generic monodromy in GL (N,ℂ). The corresponding operator acts in the direct sum of N (n − 3) copies of L2 (S1). Its kernel has a block integrable form and is expressed in terms of fundamental solutions of n − 2 elementary 3-point Fuchsian systems whose monodromy is determined by monodromy of the relevant n-point system via a decomposition of the punctured sphere into pairs of pants. For N = 2 these building blocks have hypergeometric representations, the kernel becomes completely explicit and has Cauchy type. In this case Fredholm determinant expansion yields multivariate series representation for the tau function of the Garnier system, obtained earlier via its identification with Fourier transform of Liouville conformal block (or a dual Nekrasov–Okounkov partition function). Further specialization to n = 4 gives a series representation of the general solution to Painlevé VI equation.