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Representation Theory of Quantized Gieseker Varieties, I
Ch. 11. P. 273–314.
Лосев И. В.
We study the representation theory of quantizations of Gieseker moduli spaces. We describe the categories of finite dimensional representations for all parameters and categories O for special values of parameters. We find the values of parameters, where the quantizations have finite homological dimension, and establish abelian localization theorem. We describe the two-sided ideals. Finally, we determine annihilators of the irreducible objects in categories O for some special choices of one-parameter subgroups.
Publication based on the results of:
In book
Kac, V., Popov, Vladimir L. Vol. 326. , Copyright Holder Springer Nature Switzerland AG, 2018.
Vasilev A., Kapitanov A., Roman Solovyev et al., PeerJ Computer Science 2026 Vol. 12 Article 3724
This article introduces MinMAE, a novel activation calibration method for Post-Training Quantization (PTQ) that significantly reduces accuracy loss in Convolutional Neural Networks (CNN). Motivated by the need for high-fidelity quantization without costly retraining, MinMAE directly minimizes the Mean Absolute Error (MAE) between original and dequantized activations, making it robust to outliers that degrade standard methods. ...
Added: May 3, 2026
Osipov D., / Series arXiv "math". 2022. No. 1.
This paper devotes to comparison of different cod- ing schemes (various constructions of Polar and LDPC codes, Product codes and BCH codes) for the case when information is transmitted over AWGN channel with quantization with lowest possible complexity and resolution: 1-bit. We examine performance (in terms of Frame-error-rate — FER) for schemes mentioned above and ...
Added: December 27, 2022
Etingof P., Krylov V., Losev I. et al., Mathematische Zeitschrift 2021 Vol. 297 P. 1593–1621
We study the minimally supported representations of quantizations of Gieseker moduli spaces. We relate them to SL_n-equivariant D-modules on the nilpotent cone of sl_n and to minimally supported representations of type A rational Cherednik algebras. Our main result is character formulas for minimally supported representations of quantized Gieseker moduli spaces. ...
Added: January 10, 2022
Cham: Birkhäuser, 2020.
The book consists of articles based on the XXXVIII Białowieża Workshop on Geometric Methods in Physics, 2019. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, ...
Added: November 3, 2021
Eduard Gorbunov, Kovalev D., Makarenko D. et al., , in: Advances in Neural Information Processing Systems 33 (NeurIPS 2020).: Curran Associates, Inc., 2020. P. 20889–20900.
Added: December 7, 2020
Feigin B. L., Russian Mathematical Surveys 2017 Vol. 72 No. 4 P. 707–763
This paper discusses the main known constructions of vertex operator algebras. The starting point is the lattice algebra. Screenings distinguish subalgebras of lattice algebras. Moreover, one can construct extensions of vertex algebras. Combining these constructions gives most of the known examples. A large class of algebras with big centres is constructed. Such algebras have applications ...
Added: November 5, 2020
Feigin B. L., Jimbo M., Mukhin E., Journal of Mathematical Physics 2019 Vol. 60 No. 7 P. 073507-1–073507-16
We discuss the quantization of the ̂ sl 2 coset vertex operator algebra W D(2,1;α) using the bosonization technique. We show that after quantization, there exist three families of commuting integrals of motion coming from three copies of the quantum toroidal algebra associated with gl 2 . ...
Added: December 10, 2019
Le Gouic T., Paris Q., Electronic journal of statistics 2018 Vol. 12 No. 2 P. 4239–4263
In this paper, we define and study a new notion of stability for the k-means clustering scheme building upon the field of quantization of a probability measure. We connect this definition of stability to a geometric feature of the underlying distribution of the data, named absolute margin condition, inspired by recent works on the subject. ...
Added: November 9, 2018
Grachev A., Ignatov D. I., Savchenko A., , in: Pattern Recognition and Machine Intelligence. 7th International Conference, PReMI 2017, Kolkata, India, December 5-8, 2017, Proceedings. Lecture Notes in Computer Science book series (LNCS, volume 10597).: Springer, 2017. P. 351–357.
In this paper, we consider several compression techniques for the language modeling problem based on recurrent neural networks (RNNs). It is known that conventional RNNs, e.g., LSTM-based networks in language modeling, are characterized with either high space complexity or substantial inference time. This problem is especially crucial
for mobile applications, in which the constant interaction with ...
Added: October 14, 2018
Sofia: Avangard Prima, 2018.
Added: January 31, 2018
Losev Ivan, Compositio Mathematica 2017 Vol. 153 No. 12 P. 2445–2481
In this paper we study categories O over quantizations of symplectic resolutions admitting Hamiltonian tori actions with finitely many fixed points. In this generality, these categories were introduced by Braden, Licata, Proudfoot and Webster. We establish a family of standardly stratified structures (in the sense of the author and Webster) on these categories O. We ...
Added: October 15, 2017
Karasev M., Russian Journal of Mathematical Physics 2016 Vol. 23 No. 4 P. 483–489
We discuss two examples of classical mechanical systems which can become quantum either because of degeneracy of an integral of motion or because of tuning parameters at resonance. In both examples, the commutativity of the symmetry algebra is breaking, and noncommutative symmetries arise. Over the new noncommutative algebra, the system can reveal its quantum behavior ...
Added: October 22, 2016
Akbarov S. S., Izvestiya. Mathematics 1995 Vol. 59 No. 2 P. 47–62
Added: September 23, 2016
Sergeev A., European Mathematical Society Publishing house, 2014.
This book is based on a lecture course given by the author at the Educational Center of the Steklov Mathematical Institute in 2011. It is designed for a one-semester course for undergraduate students familiar with basic differential geometry and complex and functional analysis.
The universal Teichmüller space T is the quotient of the space of quasisymmetric ...
Added: April 9, 2015
Bezrukavnikov R., Finkelberg M. V., Cambridge Journal of Mathematics 2014 Vol. 2 No. 2 P. 163–190
Marc Haiman has reduced Macdonald Positivity Conjecture to a statement about geometry of the Hilbert scheme of points on the plane, and formulated a generalization of the conjecture where the symmetric group is replaced by the wreath product of S_n and Z/rZ. He has proven the original conjecture by establishing the geometric statement about the ...
Added: December 20, 2014
Chebotarev A., Tlyachev T. V., Mathematical notes 2014 Vol. 95 No. 5 P. 721–737
In this paper, we present a purely algebraic construction of the normal factorization of multimode squeezed states and calculate their inner products. This procedure allows one to orthonormalize bases generated by squeezed states. We calculate several correct representations of the normalizing constant for the normal factorization, discuss an analog of the Maslov index for squeezed ...
Added: June 4, 2014
Finkelberg M. V., Rybnikov L. G., Algebraic Geometry 2014 Vol. 1 No. 2 P. 166–180
Drinfeld zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of an affine Lie algebra g^. In case g is the symplectic Lie algebra spN, we introduce an affine, reduced, irreducible, normal quiver variety Z which maps to the zastava space isomorphically in characteristic 0. The natural Poisson structure on ...
Added: October 25, 2013
Pereskokov A., Липская А. В., Вестник Московского энергетического института 2011 № 6 С. 30
Рассмотрены радиально-симметричные решения уравнения типа Хартри, содержащего интегральную нелинейность с потенциалом взаимодействия Юкавы, а также кулоновский потенциал. В квазиклассическом приближении выведена и исследована система уравнений для самосогласованного потенциала. Выписано правило квантования типа Бора-Зоммерфельда. Найдены асимптотические собственные значения и собственные функции, локализованные в шаре. ...
Added: December 16, 2012
Pereskokov A., Липская А. В., Вестник Московского энергетического института 2010 № 6 С. 99–109
Рассмотрены радиально-симметричные решения уравнения типа Хартри, содержащего как кулоновский потенциал, так и интегральную нелинейность с потенциалом взаимодействия Юкавы. В квазиклассическом приближении выведены и исследованы уравнения для самосогласованного потенциала. Выписано правило квантования типа Бора-Зоммерфельда. Найдены асимптотические собственные значения и собственные функции. ...
Added: December 16, 2012
Takasaki K., Takebe T., Теоретическая и математическая физика (Российская Федерация) 2012 Vol. 171 No. 2 P. 683–690
We briefly review a recursive construction of hbar-dependent solutions of the Kadomtsev-Petviashvili hierarchy. We give recurrence relations for the coefficients X_n of an ħ-expansion of the operator X = X_0 + hbar X_1 + hbar^2 X_2 + ... for which the dressing operator W is expressed in the exponential form W = exp(X/hbar). The wave ...
Added: June 22, 2012