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Фейгин Борис Львович

Факультет математики

Профиль на hse.ru ↗ тел.: +7 (495) 772-95-90 | 15320
Публикаций
147
Языков
1
Наград
11
Конференций
1
Профиль Публикации (147) Курсы (4)

Профессиональные интересы

представления тороидальных алгебркомбинторика плоских разбиений

Должности

  • Главный научный сотрудник — Факультет математики
  • профессор — Факультет математики
  • Руководитель научного коллектива — Факультет математики

Био

  • · Начал работать в НИУ ВШЭ в 2009 году.
  • · Научно-педагогический стаж: 42 года.

Образование

  • 2022 · Член-корреспондент РАН
  • 1996 · Доктор физико-математических наук: Институт теоретической физики им. Л.Д. Ландау РАН, специальность 01.00.00 «Физико-математические науки»
  • 1983 · Кандидат физико-математических наук: Санкт-Петербургское отделение математического института им. В.А. Стеклова РАН, специальность 01.00.00 «Физико-математические науки»
  • 1979 · Аспирантура: Ярославский государственный университет им. П.Г. Демидова, специальность «Математика»
  • 1974 · Специалитет: Московский государственный университет им. М.В. Ломоносова, специальность «Математика», квалификация «Математик»

Опыт работы

  • · 2009: Работает в НИУ ВШЭ с года

Награды и поощрения

  • · Медаль "Признание - 15 лет успешной работы" НИУ ВШЭ (март 2024)
  • · Благодарность НИУ ВШЭ (декабрь 2023)
  • · Благодарность Высшей школы экономики (сентябрь 2021)
  • · Благодарность Министра экономического развития Российской Федерации (сентябрь 2017)
  • · Почетная грамота Высшей школы экономики (январь 2014)
  • · Надбавка за публикацию в международном рецензируемом научном издании (2020–2022, 2018–2020)
  • · Надбавка за регулярные публикации в международных рецензируемых научных изданиях (2021–2026)
  • · Надбавка за статью в зарубежном рецензируемом журнале (2014–2016, 2012–2014)
  • · Надбавка за статью в зарубежном рецензируемом научном издании (2016–2018)
  • · Лучший преподаватель — 2012
  • · Лауреат премии "Золотая Вышка" 2014 в номинации Достижения в науке

Гранты и проекты

  • — · на соискание учёной степени кандидата наук

Конференции (1)

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  • · 2017: Transformation groups 2017 (Москва). Доклад: Shifted toroidal algebras and corresponding vertex operator algebra

Идентификаторы исследователя

Публикации (147)

Plane partitions with a “pit”: generating functions and representation theory

2018 · ARTICLE · en

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 these representations. The resulting formulas resemble formulas for characters of tensor representations of Lie superalgebra gl_{m|n}. We discuss representation theoretic interpretation of our formulas using q-deformed W-algebra gl_{m|n}.

DOI ↗ PDF ↗

Finite Type Modules and Bethe Ansatz Equations

2017 · ARTICLE · en

We introduce and study a category (Formula presented.) of modules of the Borel subalgebra (Formula presented.) of a quantum affine algebra (Formula presented.), where the commutative algebra of Drinfeld generators (Formula presented.), corresponding to Cartan currents, has finitely many characteristic values. This category is a natural extension of the category of finite-dimensional (Formula presented.) modules. In particular, we classify the irreducible objects, discuss their properties, and describe the combinatorics of the q-characters. We study transfer matrices corresponding to modules in (Formula presented.). Among them, we find the Baxter (Formula presented.) operators and (Formula presented.) operators satisfying relations of the form (Formula presented.). We show that these operators are polynomials of the spectral parameter after a suitable normalization. This allows us to prove the Bethe ansatz equations for the zeroes of the eigenvalues of the (Formula presented.) operators acting in an arbitrary finite-dimensional representation of (Formula presented.).

DOI ↗ PDF ↗

Integrals of motion from quantum toroidal algebras

2017 · ARTICLE · en

We identify the Taylor coefficients of the transfer matrices corresponding to quantum toroidal algebras with the elliptic local and non-local integrals of motion introduced by Kojima, Shiraishi, Watanabe, and one of the authors. That allows us to prove the Litvinov conjectures on the Intermediate Long Wave model. We also discuss the (gl(m),gl(n)) duality of XXZ models in quantum toroidal setting and the implications for the quantum KdV model. In particular, we conjecture that the spectrum of non-local integrals of motion of Bazhanov, Lukyanov, and Zamolodchikov is described by Gaudin Bethe ansatz equations associated to affine sl(2).

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Extensions of vertex algebras. Constructions and applications

2017 · ARTICLE · en

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 to the geometric Langlands programme.

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A combinatorial formula for affine Hall–Littlewood functions via a weighted Brion theorem

2016 · ARTICLE · en

We present a new combinatorial formula for Hall–Littlewood functions associated with the affine root system of type (Formula presented.), i.e., corresponding to the affine Lie algebra (Formula presented.). 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 be viewed as a weighted sum of exponentials of integer points in a certain infinite-dimensional convex polyhedron. We derive a weighted version of Brion’s theorem and then apply it to our polyhedron to prove the formula. © 2016 Springer International Publishing

DOI ↗ PDF ↗

Branching rules for quantum toroidal gln

2016 · ARTICLE · en

We construct an analog of the subalgebra Ugl(n)⊗Ugl(m)⊂Ugl(m+n) in the setting of quantum toroidal algebras and study the restrictions of various representations to this subalgebra.

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Coupling of two conformal field theories and Nakajima-Yoshioka blow-up equations

2016 · ARTICLE · en

We study the conformal vertex algebras which naturally arise in relation to the Nakajima–Yoshioka blow-up equations.

DOI ↗ PDF ↗

A Combinatorial Formula for Affine Hall-Littlewood Functions via a Weighted Brion Theorem

2015 · PREPRINT · en

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 be viewed as a weighted sum of exponentials of integer points in a certain infinite-dimensional convex polyhedron. We derive a weighted version of Brion's theorem and then apply it to our polyhedron to prove the formula.

Quantum toroidal gl1 and Bethe ansatz

2015 · ARTICLE · en

We establish the method of Bethe ansatz for the XXZ type model obtained from the R matrix associated to quantum toroidal gl1. We do this by using shuffle realizations of the modules and by showing that the Hamiltonian of the model is obtained from a simple multiplication operator by taking an appropriate quotient. We expect this approach to be applicable to a wide variety of models. © 2015 IOP Publishing Ltd.

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A Simple Proof of the Formula for the Betti Numbers of the Quasihomogeneous Hilbert Schemes

2015 · ARTICLE · en

In a recent paper, the first two authors proved that the generating series of the Poincare polynomials of the quasihomogeneous Hilbert schemes of points in the plane has a simple decomposition in an infinite product. In this paper, we give a very short geometrical proof of that formula.

DOI ↗ PDF ↗

Курсы (4)