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## Twisted Representation of Algebra of q-Difference Operators, Twisted q-W Algebras and Conformal Blocks

Cornell University
,
2019.

Bershtein M., Gonin R.

We study certain representations of quantum toroidal gl1 algebra for q=t. We construct explicit bosonization of the Fock modules F^{(n′,n)}_u with nontrivial slope n′/n. As a vector space, it is naturally identified with the basic level 1 representation of affine gln.
We also study twisted W-algebras of sln acting on these Fock modules.As an application, we prove the relation on q-deformed conformal blocks which was conjectured in the study of q-deformation of isomonodromy/CFT correspondence.

Bershtein M., Gonin R., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2020 Vol. 16 P. 077

We study certain representations of quantum toroidal gl1 algebra for q=t. We construct explicit bosonization of the Fock modules F^{(n′,n)}_u with nontrivial slope n′/n. As a vector space, it is naturally identified with the basic level 1 representation of affine gln. We also study twisted W-algebras of sln acting on these Fock modules.As an application, ...

Added: October 31, 2020

Bershtein M., Tsymbaliuk A., Journal of Pure and Applied Algebra 2019 Vol. 223 No. 2 P. 867-899

This paper concerns the relation between the quantum toroidal algebras and the affine Yangians of sln, denoted by U(n)q1,q2,q3 and Y(n)h1,h2,h3, respectively. Our motivation arises from the milestone work of Gautam and Toledano Laredo, where a similar relation between the quantum loop algebra Uq(Lg) and the Yangian Yh(g) has been established by constructing an isomorphism ...

Added: November 12, 2019

Bershtein M., Tsymbaliuk A., / Cornell University. Series arXiv "math". 2015. No. 1512.09109.

This paper concerns the relation between the quantum toroidal algebras and the affine Yangians of $\mathfrak{sl}_n$, denoted by $\mathcal{U}^{(n)}_{q_1,q_2,q_3}$ and $\mathcal{Y}^{(n)}_{h_1,h_2,h_3}$, respectively. Our motivation arises from the milestone work Gautam and Toledano Laredo, where a similar relation between the quantum loop algebra U_q(L\\mathfrak{g})$ and the Yangian $Y_h(\mathfrak{g})$ has been established by constructing an isomorphism of ...

Added: March 16, 2016

Bershtein M., Feigin B. L., Merzon G., Selecta Mathematica, New Series 2018 Vol. 24 No. 1 P. 21-62

We study plane partitions satisfying condition a_{n+1,m+1}=0 (this condition is called “pit”) and asymptotic conditions along three coordinate axes. We find the formulas for generating function of such plane partitions. Such plane partitions label the basis vectors in certain representations of quantum toroidal gl1 algebra, therefore our formulas can be interpreted as the characters of ...

Added: October 24, 2018

Galkin S., Belmans P., Mukhopadhyay S., / Cornell University. Series math "arxiv.org". 2020. No. 2009.05568.

We introduce graph potentials, which are Laurent polynomials associated to (colored) trivalent graphs. These graphs encode degenerations of curves to rational curves, and graph potentials encode degenerations of the moduli space of rank 2 bundles with fixed determinant. We show that the birational type of the graph potential only depends on the homotopy type of ...

Added: April 15, 2021

Feigin B. L., Jimbo M., Miwa T. et al., Journal of Algebra 2013 Vol. 380 P. 78-108

We define and study representations of quantum toroidal gln with natural bases labeled by plane partitions with various conditions. As an application, we give an explicit description of a family of highest weight representations of quantum affine gln with generic level. ...

Added: February 28, 2013

Bershtein M., Gavrylenko P., Marshakov A., / arXiv.org. Series arXiv.org "hep-th". 2017. No. 1705.00957.

We study twist-field representations of the W-algebras and generalize the construction of the corresponding vertex operators to D- and B-series. We demonstrate how the computation of characters of such representations leads to the nontrivial identities involving lattice theta-functions. We propose a construction of their exact conformal blocks, which for D-series express them in terms of ...

Added: May 4, 2017

Malyshev D., Journal of Applied and Industrial Mathematics 2020 Vol. 14 No. 4 P. 706-721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021

P. : Université Paris 13 - Paris Sorbonne Cité, 2013

In this workshop we will bring together participants who have solutions for one or more of the following problems: How can mutual understanding be optimized with the help of technology in hospitals where both patients and professionals have varying language skills, cultural backgrounds and cognitive capacities? Can domain ontologies, natural language processing tools, multilingual knowledge-based ...

Added: December 18, 2014

Danilov V., Rakhel M., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 179-187

In this paper, we show how to construct an asymptotic representation of the fundamental solution to the Cauchy problem for degenerate linear parabolic equations. ...

Added: June 6, 2021

Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293

Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...

Added: September 29, 2014

Marshirov V. V., Marshirova L. E., Сибирский журнал индустриальной математики 2013 Т. XVI № 4 С. 111-120

The paper considers the problem of determining the rate of cooling of metal during solidification at the intersection of the liquidus temperature under intense heat sink from the surface. The solution to this problem it is necessary to determine the process conditions, the boundary and initial conditions for which it is possible to get new ...

Added: November 17, 2013

Akopov A. S., Beklaryan L. A., Saghatelyan A. K., Environmental Modelling and Software 2019 Vol. 116 P. 7-25

Urban greenery such as trees can effectively reduce air pollution in a natural and eco-friendly way. However, how to spatially locate and arrange greenery in an optimal way remains as a challenging task. We developed an agent-based model of air pollution dynamics to support the optimal allocation and configuration of tree clusters in a city. The Pareto ...

Added: February 24, 2019

Malyshev D., Alekseev V., Дискретный анализ и исследование операций 2008 Т. 15 № 1 С. 3-10

Доказывается полиномиальная разрешимость задачи о независимом множестве для бесконечного семейства подмножеств класса планарных графов. ...

Added: August 31, 2012

Chernyshev S. V., Cherepanov E. A., Pankratiev E. V. et al., Journal of Mathematical Sciences 2005 Vol. 128 No. 6 P. 3487-3495

Added: January 27, 2014

Skoptsov K. A., Sheshenin S., Galatenko V. V. et al., International Journal of Applied Mechanics 2016 Vol. 8 No. 2 P. 1650016-01-1650016-18

We present a method for evaluating elastic properties of a composite material produced by molding a resin filled with short elastic fibers. A flow of the filled resin is simulated numerically using a mesh-free method. After that, assuming that spatial distribution and orientation of fibers are not significantly changed during polymerization, effective elastic moduli of ...

Added: May 22, 2016

Malyshev D., Discrete Mathematics 2015 Vol. 338 No. 11 P. 1860-1865

We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. ...

Added: April 7, 2014

Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...

Added: March 13, 2016

Gasnikov A., Maximov Y., Дорн Ю. В., Математическое моделирование 2016 Т. 28

В работе рассматриваются две потенциальные игры загрузки: модель Бэкмана (1955) и ее вырожденный вариант – модель стабильной динамики (Нестеров–де Пальма, 1998). В статье мы опишем эффективные численные процедуры поиска равновесий в этих играх. Для модели (игры) Бэкмана будет использован метод Франк–Вульфа, а для модели ста- бильной динамики используется переход к двойственной задаче. Эта задача решается ...

Added: October 23, 2015

Logvenkov S. A., Штейн А. А., Российский журнал биомеханики 2013 Т. 17 № 4 С. 47-57

The mathematical modelling is performed to study the effect of the permeability of the Casparian bands to water and solutes on the formation of the root pressure. It is shown that the pressure in the xylem vessels which stops the flow across a root cut (root pressure) decreases with increase in the permeability of the ...

Added: January 30, 2014

Nicol R., Chapman S., Vertes P. et al., Journal of Neurophysiology (США) 2012 Vol. 107 No. 5 P. 1421-1430

How do human brain networks react to dynamic changes in the sensory environment? We measured rapid changes in brain network organization in response to brief, discrete, salient auditory stimuli. We estimated network topology and distance parameters in the immediate central response period, <1 s following auditory presentation of standard tones interspersed with occasional deviant tones ...

Added: October 23, 2014

Decrouez G. G., Robinson A., Risk Analysis: An International Journal 2013 Vol. 33 No. 12 P. 2142-2153

We propose a new modeling approach for inspection data that provides a more useful interpretation of the patterns of detections of invasive pests, using cargo inspection as a motivating example. Methods that are currently in use generally classify shipments according to their likelihood of carrying biosecurity risk material, given available historical and contextual data. Ideally, ...

Added: September 29, 2014

Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291

The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...

Added: December 7, 2013

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016