Денис Борисович Углов

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Денис Борисович Углов, выдающийся специалист по теоретической и математической физике. Выпускник физфака МГУ. Доктор философии (PhD теоретическая физика), Университет Стони Брук (Stony Brook University, N.Y. USA), профессор университета Киото (Research Institute for Mathematical Sciences, Kyoto University).

Д.Б. Углов — автор десятков работ по математической физике, теории представлений бесконечномерных квантовых алгебр, точно-решаемых моделей статистической механики.

Результаты работ Д.Б. Углова используются в изучении конформных теорий поля, теории суперсимметричных калибровочных полей, в теории представлений квантовых афинных алгебр.

«Collected papers of Denis B. Uglov». Kyoto : Research Institute for Mathematical Sciences, Kyoto University, 2001.

Список статей из Arxiv.org

  1. arXiv:math/9905196  [pdf, ps, other]  math.QA Canonical bases of higher-level q-deformed Fock spaces and Kazhdan-Lusztig polynomials Authors: Denis Uglov Abstract: The aim of this paper is to generalize several aspects of the recent work of Leclerc-Thibon and Varagnolo-Vasserot on the canonical bases of the level 1 q-deformed Fock spaces due to Hayashi. Namely, we define canonical bases for the higher-level q-deformed Fock spaces of Jimbo-Misra-Miwa-Okado and establish a relation between these bases and (parabolic) Kazhdan-Lusztig polynomials for the affin…
  2. arXiv:math/9901032  [pdf, ps, other]  math.QA Canonical bases of higher-level q-deformed Fock spaces Authors: Denis Uglov Abstract: We define canonical bases of the higher-level q-deformed Fock space modules of the affine Lie algebra sl(n)^. This generalizes the result of Leclerc and Thibon for the case of level 1. We express the transition matrices between the canonical bases and the natural bases of the Fock spaces in terms of affine Kazhdan-Lusztig polynomials.
  3. arXiv:math/9806134  [pdf, ps, other]  math.QA Representations of the Quantum Toroidal Algebra on highest weight modules of the Quantum Affine Algebra of type gl(N) Authors: K. Takemura, D. Uglov Abstract: A representation of the Quantum Toroidal Algebra of type sl(N) is constructed on every irreducible integrable highest weight module of the Quantum Affine Algebra of type gl(N). As an intermediate step in the construction, we obtain a quantum analogue of the classical level-rank duality, describing the reciprocal decomposition of the q-Fock space with respect to mutually commutative actions of U_… ▽ More
  4. arXiv:math/9802048  [pdf, ps, other]  math.QA Yangian actions on higher level irreducible integrable modules of affine gl(N) Authors: Denis Uglov Abstract: An action of the Yangian of the general Lie algebra gl(N) is defined on every irreducible integrable highest weight module of affine gl(N) with level greater than 1. This action is derived, by means of the Drinfeld duality and a subsequent semi-infinite limit, from a certain induced representation of the degenerate double affine Hecke algebra H. Each vacuum module of affine gl(N) is decomposed i… ▽ More
  5. arXiv:q-alg/9705010  [pdf, ps, other]  math.QA Symmetric functions and the Yangian decomposition of the Fock and Basic modules of the affine Lie algebra \hat{sl(N)} Authors: Denis Uglov Abstract: The decompositions of the Fock and Basic modules of the affine Lie algebra \hat{sl(N)} into irreducible submodules of the Yangian algebra Y(gl(N)) are constructed. Each of the irreducible submodules admits the unique up to normalization eigenbasis of the maximal commutative subalgebra of the Yangian. The elements of this eigenbasis are identified with specializations of Macdonald symmetric funct… ▽ More
  6. arXiv:q-alg/9702024  [pdf, ps, other]  math.QA Toroidal actions on level 1 modules of U_q(\hat{sl_n}) Authors: Y. Saito, K. Takemura, D. Uglov Abstract: Recently Varagnolo and Vasserot established that the q-deformed Fock spaces due to Hayashi, and Kashiwara, Miwa and Stern, admit actions of the quantum toroidal algebra Uq(sln,tor) (n > 2) with the level (0,1). In the present article we propose a more detailed proof of this fact then the one given by Varagnolo and Vasserot. The proof is based on certain non-trivial properties of Cherednik’s… ▽ More Report number: RIMS-1133
  7. arXiv:hep-th/9702020  [pdf, ps, other]  hep-th cond-mat.str-el math.QA doi 10.1007/s002200050283 Yangian Gelfand-Zetlin Bases, gl(N)-Jack Polynomials and computation of Dynamical Correlation Functions in the Spin Calogero-Sutherland Model Authors: Denis Uglov Abstract: We consider the gl(N)-invariant Calogero-Sutherland Models with N=1,2,3,… in a unified framework, which is the framework of Symmetric Polynomials. By the framework we mean an isomorphism between the space of states of the gl(N)-invariant Calogero-Sutherland Model and the space of Symmetric Laurent Polynomials. In this framework it becomes apparent that all gl(N)-invariant Calogero-Sutherland M… ▽ More Journal ref: Commun.Math.Phys. 193 (1998) 663-696; Commun.Math.Phys. 191 (1998) 663-696
  8. arXiv:solv-int/9611006  [pdf, ps, other]  nlin.SI hep-th math.QA doi 10.1088/0305-4470/30/10/039 The orthogonal eigenbasis and norms of eigenvectors in the Spin Calogero-Sutherland Model Authors: Kouichi Takemura, Denis Uglov Abstract: Using a technique based on the Yangian Gelfand-Zetlin algebra and the associated Yangian Gelfand-Zetlin bases we construct an orthogonal basis of eigenvectors in the Calogero-Sutherland Model with spin, and derive product-type formulas for norms of these eigenvectors. Report number: RIMS-1114
  9. arXiv:q-alg/9607031  [pdf, ps, other]  math.QA Level-0 action of U_q(\hat{sl_n}) on the q-deformed Fock spaces Authors: Kouichi Takemura, Denis Uglov Abstract: On the level-1 Fock space modules of the algebra Uq(sln^) we define a level-0 action U0 of the Uq(sln^), and an action of an abelian algebra of conserved Hamiltonians commuting with the U0. An irreducible decomposition of the Fock space with respect to the level-0 action is derived by constructing a base of the Fock space in terms of the Non-symmetric Macdonald Polynomial… ▽ More
  10. arXiv:hep-th/9601170  [pdf, ps, other]  hep-th doi 10.1016/0550-3213(96)00387-2 Semi-infinite wedges and the conformal limit of the fermionic Calogero-Sutherland Model with spin 12 Authors: Denis Uglov Abstract: The conformal limit over an anti-ferromagnetic vacuum of the fermionic spin 12 Calogero-Sutherland Model is derived by using the wedge product formalism. The space of states in the conformal limit is identified with the Fock space of two complex fermions, or, equivalently, with a tensor product of an irreducible level-1 module of $\slt$ and a Fock space module of the Heisenberg algeb… ▽ More Journal ref: Nucl.Phys. B478 (1996) 401-430
  11. arXiv:hep-th/9508145  [pdf, ps, other]  hep-th The trigonometric counterpart of the Haldane Shastry Model Authors: Denis Uglov Abstract: The hierarchy of Integrable Spin Chain Hamiltonians, which are trigonometric analogs of the Haldane Shastry Model and of the associated higher conserved charges, is derived by a reduction from the trigonometric Dynamical Models of Bernard-Gaudin-Haldane-Pasquier. The Spin Chain Hamiltonians have the property of Uq(gl^2)-invariance. The spectrum of the Hamiltonians and the… ▽ More
  12. arXiv:hep-th/9502068  [pdf, ps, other]  hep-th doi 10.1007/BF02189226 sl(N) Onsager’s Algebra and Integrability Authors: D. Uglov, I. Ivanov Abstract: We define an sl(N) analog of Onsager’s Algebra through a finite set of relations that generalize the Dolan Grady defining relations for the original Onsager’s Algebra. This infinite-dimensional Lie Algebra is shown to be isomorphic to a fixed point subalgebra of sl(N) Loop Algebra with respect to a certain involution. As the consequence of the generalized Dolan Grady relations a Hamiltonia… ▽ More
  13. arXiv:hep-th/9409155  [pdf, ps, other]  hep-th doi 10.1016/0375-9601(95)00143-Q Finite-difference representations of the degenerate affine Hecke algebra Authors: D. Uglov Abstract: The representations of the degenerate affine Hecke algebra in which the analogues of the Dunkl operators are given by finite-difference operators are introduced. The non-selfadjoint lattice analogues of the spin Calogero-Sutherland hamiltonians are analysed by Bethe-Ansatz. The sl(m)-Yangian representations arising from the finite-difference representations of the degenerate affine Hecke alge… ▽ More
  14. arXiv:cond-mat/9403066  [pdf, ps, other]  cond-mat hep-th doi 10.1016/0375-9601(94)90074-4 Correlation Function of the Spin-1/2 XXX Antiferromagnet Authors: Vladimir E. Korepin, Anatoli G. Izergin, Fabian H. L. Essler, Denis B. Uglov Abstract: We consider a special correlation function in the isotropic spin-$\half$ Heisenberg antiferromagnet. It is the probability of finding a ferromagnetic string of (adjacent) spins in the antiferromagnetic ground state. We give two different representations for this correlation function. Both of them are exact at any distance, but one becomes more effective for the description of long distance behav… ▽ More Journal ref: Phys.Lett. A190 (1994) 182-184
  15. arXiv:hep-th/9310158  [pdf, ps, other]  hep-th cond-mat doi 10.1016/0375-9601(94)90748-X The Yangian symmetry of the Hubbard Model Authors: D. B. Uglov, V. E. Korepin Abstract: We discovered new hidden symmetry of the one-dimensional Hubbard model. We showthat the one-dimensional Hubbard model on the infinite chain has the infinite-dimensional algebra of symmetries. This algebra is a direct sum of two sl(2)-Yangians. This Y(sl(2))⊕Y(sl(2)) symmetry is an extension of the well-known sl(2)⊕sl(2) . The deformation parameters of the Yangians are e… ▽ More Journal ref: Phys.Lett. A190 (1994) 238-242
  16. arXiv:hep-th/9302139  [pdf, ps, other]  hep-th math.QA doi 10.1007/BF00750306 The quantum bialgebra associated with the eight-vertex R-matrix Authors: D. B. Uglov Abstract: The quantum bialgebra related to the Baxter’s eight-vertex R-matrix is found as a quantum deformation of the Lie algebra of sl(2)-valued automorphic functions on a complex torus. Journal ref: Lett.Math.Phys. 28 (1993) 139-142
  17. arXiv:hep-th/9302138  [pdf, ps, other]  hep-th math.QA doi 10.1007/BF00751172 The Lie algebra of sl(2)-valued automorphic functions on a torus Authors: D. B. Uglov Abstract: It is shown that the Lie algebra of the automorphic, meromorphic sl(2, C) -valued functions on a torus is a geometric realization of a certain infinite-dimensional finitely generated Lie algebra. In the trigonometric limit, when the modular parameter of the torus goes to zero, the former Lie algebra goes over into the sl(2,C) -valued loop algebra, while the latter one — into the Lie algebra (sl(… ▽ More Submitted 26 February, 1993; originally announced February 1993. Comments: 13 pages Journal ref: Lett.Math.Phys. 31 (1994) 65-76
  18. arXiv:hep-th/9203037  [pdf, ps, other]  hep-th math.QA nlin.SI doi 10.1016/0375-9601(92)90605-L R-matrices for the semicyclic representations of U_q sl^(2) Authors: I. T. Ivanov, D. B. Uglov Abstract: R-matrices for the semicyclic representations of U_qsl^(2) are found as a limit in the checkerboard chiral Potts model. Submitted 13 March, 1992; originally announced March 1992. Journal ref: Phys.Lett. A167 (1992) 459-464