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## Highest-weight vectors and three-point functions in GKO coset decomposition

Cornell University
,
2024.

We revisit the classical Goddard-Kent-Olive coset construction. We find the formulas for the highest weight vectors in coset decomposition and calculate their norms. We also derive formulas for matrix elements of natural vertex operators between these vectors. This leads to relations on conformal blocks. Due to the AGT correspondence, these relations are equivalent to blowup relations on Nekrasov partition functions with the presence of the surface defect. These relations can be used to prove Kyiv formulas for the Painlevé tau-functions (following Nekrasov's method).

Priority areas:
mathematics

Language:
English

Covolo T., Ovsienko V., Poncin N., Journal of Geometry and Physics 2012 Vol. 62 P. 2294–2319

We define the notions of trace, determinant and, more generally, Berezinian of matrices over a (Z_2)^n graded commutative associative algebra. The applications include a new approach to the classical theory of matrices with coefficients in a Clifford algebra, in particular of quaternionic matrices. In a special case, we recover the classical Dieudonn\'e determinant of quaternionic ...

Added: September 28, 2015

Khoroshkin S. M., Shapiro A., Journal of Geometry and Physics 2010 Vol. 60 No. 11 P. 1833–1851

In this article, we give an explicit formula for the universal weight function of the quantum twisted affine algebra Uq(A(2)2 ). The calculations use the technique of projecting products of Drinfeld currents onto the intersection of Borel subalgebras of different types. ...

Added: September 26, 2012

Providence: American Mathematical Society, 2014

Added: September 15, 2016

Braverman A., Michael Finkelberg, Nakajima H., / Cornell University. Series math "arxiv.org". 2014.

We describe the (equivariant) intersection cohomology of certain moduli spaces ("framed Uhlenbeck spaces") together with some structures on them (such as e.g.\ the Poincar\'e pairing) in terms of representation theory of some vertex operator algebras ("W-algebras"). ...

Added: January 30, 2015

Levin A., Olshanetsky M., Zotov A., / Cornell University. Series math "arxiv.org". 2014.

e describe classical top-like integrable systems arising from the quantum
exchange relations and corresponding Sklyanin algebras. The Lax operator is
expressed in terms of the quantum non-dynamical $R$-matrix even at the
classical level, where the Planck constant plays the role of the relativistic
deformation parameter in the sense of Ruijsenaars and Schneider (RS). The
integrable systems (relativistic tops) are described ...

Added: January 23, 2015

Marshakov A., Journal of Geometry and Physics 2012 Vol. 003 P. 16–36

We discuss the Poisson structures on Lie groups and propose an explicit construction of the integrable models on their appropriate Poisson submanifolds. The integrals of motion for the SL(N)-series are computed in cluster variables via the Lax map. This construction, when generalised to the co-extended loop groups, gives rise not only to alternative descriptions of relativistic Toda systems, but allows ...

Added: February 11, 2013

Khoroshkin A., Markaryan N. S., Shadrin S., / Cornell University. Series math "arxiv.org". 2012. No. 1206.3749.

We give an explicit formula for a quasi-isomorphism between the operads Hycomm (the homology of the moduli space of stable genus 0 curves) and BV/Δ (the homotopy quotient of Batalin-Vilkovisky operad by the BV-operator). In other words we derive an equivalence of Hycomm-algebras and BV-algebras enhanced with a homotopy that trivializes the BV-operator. These formulas ...

Added: August 29, 2012

S.M. Khoroshkin, M. G. Matushko, Journal of Mathematical Physics 2019 Vol. 60 No. 7 P. 071706-1–071706-22

We present a construction of an integrable model as a projective type limit of Calogero-Sutherland models of N fermionic particles, when N tends to infinity. Explicit formulas for limits of Dunkl operators and of commuting Hamiltonians by means of vertex operators are given. ...

Added: September 19, 2019

A. Levin, Olshanetsky M., Zotov A., Journal of High Energy Physics 2014 Vol. 2014 No. 7:12 P. 1–39

We describe classical top-like integrable systems arising from the quantum exchange relations and corresponding Sklyanin algebras. The Lax operator is expressed in terms of the quantum non-dynamical R-matrix even at the classical level, where the Planck constant plays the role of the relativistic deformation parameter in the sense of Ruijsenaars and Schneider (RS). The integrable ...

Added: January 23, 2015

Akhmedov E., Physical Review D - Particles, Fields, Gravitation and Cosmology 2013 Vol. 87 No. 4 P. 044049

Following Krotov and Polyakov [ Nucl. Phys. B849 410 (2011)], we show that in global de Sitter space its isometry is broken by the loop IR divergences for any invariant vacuum state of the massive scalars. We derive a kinetic equation in global de Sitter space that follows from the Dyson-Schwinger equation of the Schwinger-Keldysh ...

Added: February 27, 2013

Belavin V., Geiko R., Journal of High Energy Physics 2017 Vol. 125 P. 1–13

We continue to investigate the dual description of the Virasoro conformal blocks arising in the framework of the classical limit of the AdS3/CFT2 correspondence. To give such an interpretation in previous studies, certain restrictions were necessary. Our goal here is to consider a more general situation available through the worldline approximation to the dual AdS gravity. ...

Added: August 31, 2017

Arseyev P., Mantsevich V. N., Maslova N. S., JETP Letters 2011 Vol. 94 No. 5 P. 422–428

We present theoretical investigation of spatial charge distribution in the two-level system with strong Coulomb correlations by means of Heisenberg equations analysis for localized states total electron filling numbers taking into account pair correlations of local electron density. It was found that tunneling current through nanometer scale structure with strongly coupled localized states causes Coulomb ...

Added: October 28, 2014

Буров А.А., Герман А. Д., Косенко И. И., Космические исследования 2014 Т. 52 № 4 С. 307–312

The problem of planar oscillations of a pendulum with variable length suspended on the Moon’s surface is considered. It is assumed that the Earth and Moon (or, in the general case, a planet and its satellite, or an asteroid and a spacecraft) revolve around the common center of mass in unperturbed elliptical Keplerian orbits. We ...

Added: November 8, 2014

BOSSY M., Jabir J. M., Electronic Communications in Probability 2018 Vol. 23 P. 1–14

In this paper, we prove a particle approximation, in the sense of the propagation of chaos, of a Lagrangian stochastic model submitted to specular boundary condition and satisfying the mean no-permeability condition. ...

Added: June 7, 2018

Пенза: ПГУ, 2015

В сборник трудов включены доклады юбилейного ХХ-го Международного симпозиума «Надежность и качество», проходившего с 25 по 31 мая 2015 г. в городе Пензе.
Рассмотрены актуальные проблемы теории и практики повышения надежности и качества; эффективности внедрения инновационных и информационных технологий в фундаментальных научных и прикладных исследованиях, образовательных и коммуникативных системах и средах, экономике и юриспруденции; методов и ...

Added: May 31, 2015

Sergeev A., Васильев А. Ю., Russian Mathematical Surveys 2013 Vol. 68 No. 3 P. 435–502

Teichmüller theory is a ramified and rapidly developing area of mathematics which has multiple connections with other directions in the mathematical sciences and with their applications, first and foremost in mathematical physics. In this survey the main lines of development of this theory and its applications to string theory are presented in a historical context.
Bibliography: 128 titles. ...

Added: April 9, 2015

Aseeva N., Gromov E., Onosova I. V. et al., JETP Letters 2016 Vol. 103 No. 10 P. 653–657

Evolution of solitons is addressed in the framework of a third-order nonlinear Schrödinger equation (NLSE), including nonlinear dispersion, third-order dispersion and a pseudo-stimulated-Raman-scattering (pseudo-SRS) term, i.e., a spatial-domain counterpart of the SRS term, which is well known as a part of the temporal domain NLSE in optics. In this context, it is induced by the ...

Added: June 28, 2016

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65–83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

49606783, Russian Journal of Mathematical Physics 2019 Vol. 26 No. 2 P. 168–173

The parameters of unstable short-living isotopes are studied from
the mathematical point of view. The values of the chemical potential
and activity parameters that determine the neutron halo arising when
the neutron separates from the nucleus of an unstable isotope are
calculated. The analogy between nuclear physics and economics is
considered from the point of view of such parameters as ...

Added: August 25, 2019

Окубо Ю. undefined., Journal of Physics: Conference Series 2017 Vol. 804 No. 012036 P. 1–8

We investigate the existence and the orthogonality of the generalized Jack symmetric functions which play an important role in the AGT relations. We show their orthogonality by deforming them to the generalized Macdonald symmetric functions. ...

Added: October 26, 2017

Budkov Y., Journal of Physics: Condensed Matter 2019 Vol. 31 P. 078002–078003

We reply to the comment on our paper by Budkov (2018 J. Phys.: Condens. Matter 30 344001). ...

Added: January 4, 2019

Kurkina O. E., Kurkin A. A., Rouvinskaya E. et al., Письма в Журнал экспериментальной и теоретической физики 2012 Т. 95 № 2 С. 98–103

Nonlinear wave dynamics is discussed using the extended modified Korteweg–de Vries equation that includes the combination of the third- and fifth- order terms and is valid for waves in a three-layer fluid with so-called symmetric stratification. The derived equation has solutions in the form of solitary waves of various polarities. At small amplitudes, they are ...

Added: August 24, 2012

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1–16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

М.: Издательство математико-механического факультета МГУ, 2009

В настоящий сборник вошли аннотации докладов участников XVI международной конференции «Ломоносов» по секции «Математика и механика». ...

Added: February 4, 2013