?
Kac–Moody groups and cosheaves on Davis building
Journal of Algebra. 2018. Vol. 515. P. 202-235.
Румынин Д. А., Hristova K.
We investigate smooth representations of complete Kac-Moody groups. We approach representation theory via geometry, in particular, the group action on the Davis realisation of its Bruhat-Tits building. Our results include an estimate on projective dimension, localisation theorem, unimodularity and homological duality.
Keywords: buildingdualityHecke algebraProjective ResolutionKac-Moody groupsSmooth representationDavis realisationprojective dimension
Publication based on the results of:
Rumynin D., Hristova K., Capdeboscq I., Sbornik Mathematics 2020 Vol. 211 No. 8 P. 1065-1079
We initiate an investigation of lattices in a new class of locally compact groups: so-called locally pro-p-complete Kac-Moody groups. We discover that in rank 2 their cocompact lattices are particularly well-behaved: under mild assumptions, a cocompact lattice in this completion contains no elements of order p. This statement is still an open question for the Caprace-Rémy-Ronan completion. Using this, ...
Added: September 7, 2021
Feigin B. L., Jimbo M., Mukhin E., Communications in Mathematical Physics 2019 No. 367 P. 455-481
On a Fock space constructed from mn free bosons and lattice Z mn , we give a level n action of the quantum toroidal algebra E m associated to gl m , together with a level m action of the quantum toroidal algebra E n associated to gl n . We prove that the E ...
Added: December 10, 2019
Zatelepin A., Shchur L., / Cornell University. Series "Working papers by Cornell University". 2010. No. 1008.3573.
We report on numerical investigation of fractal properties of critical interfaces in two-dimensional Potts models. Algorithms for finding percolating interfaces of Fortuin-Kasteleyn clusters, their external perimeters and interfaces of spin clusters are presented. Fractal dimensions are measured and compared to exact theoretical predictions. ...
Added: March 7, 2016
Dietzenbacher B., Estévez-Fernández A., Borm P. et al., Annals of Operations Research 2020
This paper studies bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the theory on TU-bankruptcy, we introduce a duality notion for NTU-bankruptcy rules and derive several axiomatic characterizations of the proportional rule and the constrained relative equal awards rule. ...
Added: June 2, 2020
Smirnova N., Tarashnina S. I., Russian Mathematics 2016 Vol. 60 No. 6 P. 63-74
We understand a solution of a cooperative TU-game as the α-prenucleoli set, α ∈ R, which is a generalization of the notion of the [0, 1]-prenucleolus. We show that the set of all α-nucleoli takes into account the constructive power with the weight α and the blocking power with the weight (1 − α) for all possible values of the parameter α. The ...
Added: July 7, 2016
Amosov G. G., Zhdanovskiy I., Journal of Mathematical Sciences 2016 Vol. 215 No. 6 P. 659-676
We study the noncommutative operator graph ℒ θ depending on a complex parameter θ recently introduced by M. E. Shirokov to construct channels with positive quantum zero-error capacity having vanishing n-shot capacity. We define a noncommutative group G and an algebra A θ which is the quotient of ℂG by a special algebraic relation depending on θ such that ...
Added: July 8, 2016
Румынин Д. А., Kirkina K., Capdeboscq I., Forum of Mathematics, Sigma 2018 Vol. 6 P. 1-35
How many generators and relations does SL_n (F_q [t, t^{−1}]) need? In this paper we exhibit its explicit
presentation with 9 generators and 44 relations. We investigate presentations of affine Kac–Moody
groups over finite fields. Our goal is to derive finite presentations, independent of the field and with
as few generators and relations as we can achieve. It ...
Added: October 31, 2018
Rumynin D., Capdeboscq I., Journal of Algebra 2020 Vol. 561 P. 131-148
In this paper we construct a new “pro-p-complete” topological Kac-Moody group and compare it to various known topological Kac-Moody groups. We come across this group by investigating the process of completion of groups with BN-pairs. We would like to know whether the completion of such a group admits a BN-pair. We give explicit criteria for ...
Added: September 7, 2021
Kondo S., Yasuda S., Journal of Number Theory 2012 Vol. 132 No. 9 P. 1910-1948
Formulas (Theorems 3.5 and 4.1) which express the local L-factor and the local epsilon factor of an irreducible admissible representation of GL_d over a non-archimedean local field in terms of the eigenvalues of some explicitly given Hecke operators are derived. ...
Added: September 22, 2014
Smirnova N., Тарашнина С. И., Известия высших учебных заведений. Математика 2016 Т. 6 С. 63-74
As a solution concept of cooperative TU-game we propose the set of $\alpha$-prenucleoli, $\alpha\in R$, that is a generalization of the $[0,1]$-prenucleolus. In the paper we show that in a cooperative game the set of $\alpha$-prenucleoli takes into account the constructive power with weight $\alpha$ and the blocking power with weight $(1-\alpha)$ for all possible ...
Added: October 20, 2015
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017
Красноярск : ИВМ СО РАН, 2013
Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...
Added: November 18, 2013
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Grines V., Gurevich E., Pochinka O., Russian Mathematical Surveys 2017 Vol. 71 No. 6 P. 1146-1148
In the paper a Palis problem on finding sufficient conditions on embedding of Morse-Smale diffeomorphisms in topological flow is discussed. ...
Added: May 17, 2017
Okounkov A., Aganagic M., Moscow Mathematical Journal 2017 Vol. 17 No. 4 P. 565-600
We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties.
This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik Zamolodchikov and dynamical q-difference equations. ...
Added: October 25, 2018
Danilov B.R., Moscow University Computational Mathematics and Cybernetics 2013 Vol. 37 No. 4 P. 180-188
The article investigates a model of delays in a network of functional elements (a gate network) in an arbitrary finite complete basis B, where basis elements delays are arbitrary positive real numbers that are specified for each input and each set of boolean variables supplied on the other inputs. Asymptotic bounds of the form τ ...
Added: December 2, 2019
Amerik E., Verbitsky M., / Cornell University. Series arXiv "math". 2021.
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions. It was shown that the MBM loci on deformation equivalent hyperkahler manifolds are diffeomorphic. We determine the MBM loci on a hyperkahler manifold ...
Added: April 7, 2022
Litvin Y. V., Абрамов И. В., Технологии техносферной безопасности 2016 № 66
Advanced approach to the assessment of a random time of arrival fire fighting calculation on the object of protection, the time of their employment and the free combustion. There is some quantitative assessments with the review of analytical methods and simulation ...
Added: August 27, 2016
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Levashov M., Кухаренко А. В., Вопросы защиты информации 2018 № 2 С. 66-71
Рассматривается статистическая модель одного этапа системы фрод-мониторинга транзакций в интернет-банкинге. Построен и рассчитан близкий к отношению правдоподобия критерий отсева мошеннических транзакций. Для выборочных распределений, полученных на выборке объема в 1 млн реальных транзакций, вычислены параметры эффективности этого критерия. ...
Added: June 14, 2018
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
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
Arzhantsev I., Journal of Lie Theory 2000 Vol. 10 No. 2 P. 345-357
Added: July 8, 2014