• A
  • A
  • A
  • АБВ
  • АБВ
  • АБВ
  • A
  • A
  • A
  • A
  • A
Обычная версия сайта
  • RU
  • EN
  • HSE University
  • Publications
  • Articles
  • Characters of Feigin-Stoyanovsky subspaces and Brion's theorem
  • RU
  • EN
Расширенный поиск
Высшая школа экономики
Национальный исследовательский университет
Priority areas
  • business informatics
  • economics
  • engineering science
  • humanitarian
  • IT and mathematics
  • law
  • management
  • mathematics
  • sociology
  • state and public administration
by year
  • 2027
  • 2026
  • 2025
  • 2024
  • 2023
  • 2022
  • 2021
  • 2020
  • 2019
  • 2018
  • 2017
  • 2016
  • 2015
  • 2014
  • 2013
  • 2012
  • 2011
  • 2010
  • 2009
  • 2008
  • 2007
  • 2006
  • 2005
  • 2004
  • 2003
  • 2002
  • 2001
  • 2000
  • 1999
  • 1998
  • 1997
  • 1996
  • 1995
  • 1994
  • 1993
  • 1992
  • 1991
  • 1990
  • 1989
  • 1988
  • 1987
  • 1986
  • 1985
  • 1984
  • 1983
  • 1982
  • 1981
  • 1980
  • 1979
  • 1978
  • 1977
  • 1976
  • 1975
  • 1974
  • 1973
  • 1972
  • 1971
  • 1970
  • 1969
  • 1968
  • 1967
  • 1966
  • 1965
  • 1964
  • 1963
  • 1958
  • More
Subject
News
August 25, 2026
Scientists Develop Algorithm for More Reliable Processors in Data Centres
Researchers from HSE MIEM and Samara University have developed the LRF-3D algorithm to automatically bypass idle nodes in three-dimensional networks-on-chip. Thanks to its hierarchical architecture, the algorithm outperforms existing solutions in both speed and path accuracy, improving processor reliability for use in data centres, supercomputers, and AI computing. The source code and test results are publicly available.
August 24, 2026
Researchers Develop Method for Direct Generation of Regulatory DNA
Researchers at HSE University have developed a model for generating promoters and enhancers—DNA sequences that regulate gene activity. The model works directly with DNA nucleotides, without first transforming them into a continuous numerical representation. This solution could be useful for applications in synthetic biology and gene therapy. The study results were presented at the ICLR 2026 Workshop ‘Generative AI in Genomics (Gen^2): Barriers and Frontiers.’
August 21, 2026
Social Integration: At the Crossroads of Knowledge and Values
The International Laboratory for Social Integration Research (ILSIR) at HSE University studies the challenges faced by vulnerable groups and explores ways to help them participate fully in everyday life. To develop effective solutions, the laboratory’s researchers combine cutting-edge methods with practical fieldwork. In this interview with the HSE News Service, Laboratory Head Elena Iarskaia-Smirnova discusses the laboratory’s work.

 

Have you spotted a typo?
Highlight it, click Ctrl+Enter and send us a message. Thank you for your help!

Publications
  • Books
  • Articles
  • Chapters of books
  • Working papers
  • Report a publication
  • Research at HSE

?

Characters of Feigin-Stoyanovsky subspaces and Brion's theorem

Functional Analysis and Its Applications. 2015. Vol. 49. No. 1. P. 15–24.
Makhlin I.

We give an alternative proof of the main result of [1]; the proof relies on Brion’s theorem about convex polyhedra. The result itself can be viewed as a formula for the character of the Feigin-Stoyanovsky subspace of an integrable irreducible representation of the affine Lie algebra widehatsln(C). Our approach is to assign integer points of a certain polytope to vectors comprising a monomial basis of the subspace and then compute the character by using (a variation of) Brion’s theorem.

Language: English
Keywords: representation theoryconvex polytopescharacter formulasAffine Lie algebra
Similar publications
Stochastic local volatility models and the Wei-Norman factorization method
Guerrero J., Orlando G., Discrete and Continuous Dynamical Systems - Series S 2022 Vol. 15 No. 12 P. 3699–3722
In this paper, we show that a time-dependent local stochastic volatility (SLV) model can be reduced to a system of autonomous PDEs that can be solved using the heat kernel, by means of the Wei-Norman factorization method and Lie algebraic techniques. Then, we compare the results of traditional Monte Carlo simulations with the explicit solutions ...
Added: February 23, 2024
Representations and degenerations
Kiritchenko V., Dumanski I., Oberwolfach Snapshots, Germany 2022 Article SNAP-2022-007-EN
In this snapshot, we explain two important mathematical concepts (representation and degeneration) in elementary terms. We will focus on the simplest meaningful examples, and motivate both concepts by study of symmetry. ...
Added: January 31, 2023
Interactions with Lattice Polytopes Magdeburg, Germany, September 2017
Springer, 2022.
This book collects together original research and survey articles highlighting the fertile interdisciplinary applications of convex lattice polytopes in modern mathematics. Covering a diverse range of topics, including algebraic geometry, mirror symmetry, symplectic geometry, discrete geometry, and algebraic combinatorics, the common theme is the study of lattice polytopes. These fascinating combinatorial objects are a cornerstone ...
Added: January 31, 2023
Вторые когомологии регулярных полупростых многообразий Хессенберга на основе ГКМ-теории
Ayzenberg A., Масуда М., Сато Т., Труды Математического института им. В.А. Стеклова РАН 2022 Т. 317 С. 5–26
We describe the second cohomology of a regular semisimple Hessenberg variety by generators and relations explicitly in terms of GKM theory. The cohomology of a regular semisimple Hessenberg variety becomes a module of a symmetric group Sn by the dot action introduced by Tymoczko. As an application of our explicit description, we give a formula describing the ...
Added: October 27, 2022
Crystals and monodromy of Bethe vectors
Halacheva I., Kamnitzer J., Rybnikov L. G. et al., Duke Mathematical Journal 2020 Vol. 169 No. 12 P. 2337–2419
Fix a semisimple Lie algebra 𝔤. Gaudin algebras are commutative algebras acting on tensor product multiplicity spaces for 𝔤-representations. These algebras depend on a parameter in the Deligne–Mumford moduli space of marked stable genus 0 curves. When the parameter is real, then the Gaudin algebra acts with simple spectrum on the tensor product multiplicity space and gives us a ...
Added: July 22, 2020
Beilinson-Drinfeld Schubert varieties and global Demazure modules
Dumanski I., Feigin E., Finkelberg M. V., / Series math "arxiv.org". 2020. No. 2003.12930.
We compute the spaces of sections of powers of the determinant line bundle on the spherical Schubert subvarieties of the Beilinson- Drinfeld affine Grassmannians. The answer is given in terms of global Demazure modules of the current Lie algebra. ...
Added: April 2, 2020
On the functor of Arakawa, Suzuki and Tsuchiya
Khoroshkin S. M., Nazarov M., , in: Advanced Studies in Pure Mathematics (т.76 Representations Theory, Special Functions and Painleve Equations - RIMS 2015)Vol. 76.: Tokyo: Mathematical Society of Japan, 2018. Ch. 8 P. 275–302.
Arakawa, Suzuki and Tsuchiya defined a correspondence between certain modules of the trigonometric Cherednik algebra CN depending on a parameter κ∈C, and certain modules of the affine Lie algebra slˆm of level κ−m. We give a detailed proof of this correspondence by working with the affine Lie algebra glˆm alongside of slˆm. We also relate ...
Added: October 8, 2019
Advanced Studies in Pure Mathematics (т.76 Representations Theory, Special Functions and Painleve Equations - RIMS 2015)
Tokyo: Mathematical Society of Japan, 2018.
This volume is the proceedings of the conference "Representation Theory, Special Functions and Painlevé Equations" at the Research Institute for Mathematical Sciences, Kyoto University from March 3 to March 6 in 2015 ...
Added: October 8, 2019
Two-term partial tilting complexes over Brauer tree algebras
Antipov M., Звонарёва А. О., Journal of Mathematical Sciences 2014 Vol. 202 No. 3 P. 333–345
In this paper, all indecomposable two-term partial tilting complexes over a Brauer tree algebra with multiplicity 1 are described, using a criterion for a minimal projective presentation of a module to be a partial tilting complex. As an application, all two-term tilting complexes over a Brauer star algebra are described and their endomorphism rings are ...
Added: December 25, 2018
Modality of representations and geometry of θ-groups
Vladimir L. Popov, , in: Lie Groups, Geometry, and Representation Theory. A Tribute to the Life and Work of Bertram KostantVol. 326.: Copyright Holder Springer Nature Switzerland AG, 2018. Ch. 16 P. 459–479.
We first establish several general properties of modality of algebraic group actions. In particular,we introduce the notion of a modality-regular action and prove that every visible action is modality-regular. Then, using these results, we classify irreducible linear representations of connected simple algebraic groups of every fixed modality < 3. Next, exploring a finer geometric structure of linear actions, we ...
Added: October 27, 2018
Construction of Milnorian representations
Smilga I., / Series arXiv "math". 2018. No. 1802.07193.
We prove a partial converse to the main theorem of the author's previous paper "Proper affine actions: a sufficient criterion" (submitted; available at arXiv:1612.08942). More precisely, let G be a semisimple real Lie group with a representation rho on a finite-dimensional real vector space V, that does not satisfy the criterion from the previous paper. ...
Added: September 26, 2018
Generalized Weyl modules and nonsymmetric q-Whittaker functions
Feigin E., Makedonskyi I., Orr D., Advances in Mathematics 2018 Vol. 330 P. 997–1033
We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric q-Whittaker functions. In particular, we show that the series part of the nonsymmetric q-Whittaker function is a generating function for the graded characters of generalized global Weyl modules. ...
Added: September 13, 2018
Cactus Group and Monodromy of Bethe Vectors
Leonid Rybnikov, International Mathematics Research Notices 2018 No. 1 P. 202–235
Cactus group is the fundamental group of the real locus of the Deligne–Mumford moduli space of stable rational curves. This group appears naturally as an analog of the braid group in coboundary monoidal categories. We define an action of the cactus group on the set of Bethe vectors of the Gaudin magnet chain corresponding to ...
Added: February 6, 2018
Conjecture on theta-blocks of order 1
Valery Gritsenko, Wang H., Russian Mathematical Surveys 2017 Vol. 72 No. 5 P. 968–970
In this paper we prove the indicated conjecture in the last case of known infinite series of theta-blocks of weight 2. ...
Added: January 29, 2018
Гипотеза о тэта-блоках первого порядка
Gritsenko V., Ванг Х., Успехи математических наук 2017 Т. 72 № 5 С. 191–192
In this paper we prove the conjecture above in the last case of known theta-blocks of weight 2. This gives a new intereting series of Borcherds products of weight 2. ...
Added: October 11, 2017
Generalized Weyl modules
Makedonskyi I., , in: Oberwolfach reportsVol. 13. Issue 1.: Zürich: European Mathematical Society Publishing house, 2016. P. 638–639.
Report on generalized Weyl modules (joint with Evgeny Feigin) ...
Added: December 22, 2016
Generalized Weyl modules for twisted current algebras
Feigin E., Makedonskyi I., / Series math "arxiv.org". 2016. No. arXiv:1606.05219.
We introduce the notion of generalized Weyl modules for twisted current algebras. We study their representation-theoretic and combinatorial properties and connection to the theory of nonsymmetric Macdonald polynomials. As an application we compute the dimension of the classical Weyl modules in the remaining unknown case. ...
Added: June 17, 2016
Generalized Weyl modules and nonsymmetric q-Whittaker functions
Feigin E., Makedonskyi I., Orr D., / Series math "arxiv.org". 2016. No. 1605.01560.
We introduce generalized global Weyl modules and relate their graded characters to nonsymmetric Macdonald polynomials and nonsymmetric q-Whittaker functions. In particular, we show that the series part of the nonsymmetric q-Whittaker function is a generating function for the graded characters of generalized global Weyl modules. ...
Added: May 6, 2016
Vertices of FFLV polytopes
Feigin E., Makhlin I., / Series math "arxiv.org". 2016. No. arXiv:1604.08844.
FFLV polytopes describe monomial bases in irreducible representations of sln. We study various sets of vertices of FFLV polytopes. First, we prove the locality of set of vertices with respect to the type A Dynkin diagram. Second, we describe all the permutation vertices. Third, we describe all the simple vertices and prove that their number ...
Added: May 6, 2016
Recent Developments in Representation Theory
Providence: AMS, 2016.
This volume contains the proceedings of the Maurice Auslander Distinguished Lectures and International Conference, held in April 2013 and April-May 2014, in Falmouth, MA. ...
Added: October 13, 2015
A Combinatorial Formula for Affine Hall-Littlewood Functions via a Weighted Brion Theorem
Feigin B. L., Makhlin I., / Series math "arxiv.org". 2015.
We present a new combinatorial formula for Hall-Littlewood functions associated with the affine root system of type A~n−1, i.e. corresponding to the affine Lie algebra slˆn. Our formula has the form of a sum over the elements of a basis constructed by Feigin, Jimbo, Loktev, Miwa and Mukhin in the corresponding irreducible representation.Our formula can ...
Added: August 7, 2015
  • About
  • About
  • Key Figures & Facts
  • Sustainability at HSE University
  • Faculties & Departments
  • International Partnerships
  • Faculty & Staff
  • HSE Buildings
  • HSE University for Persons with Disabilities
  • Public Enquiries
  • Studies
  • Admissions
  • Programme Catalogue
  • Undergraduate
  • Graduate
  • Exchange Programmes
  • Summer University
  • Summer Schools
  • Semester in Moscow
  • Business Internship
  • Research
  • International Laboratories
  • Research Centres
  • Research Projects
  • Monitoring Studies
  • Conferences & Seminars
  • Academic Jobs
  • Yasin (April) International Academic Conference on Economic and Social Development
  • Media & Resources
  • Publications by staff
  • HSE Journals
  • Publishing House
  • iq.hse.ru: commentary by HSE experts
  • Library
  • Economic & Social Data Archive
  • Video
  • HSE Repository of Socio-Economic Information
  • HSE1993–2026
  • Contacts
  • Copyright
  • Privacy Policy
  • Site Map
Edit