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Wednesday, July 29, 2020 | History

7 edition of The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems found in the catalog.

The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems

by P. I. Etingof

  • 121 Want to read
  • 22 Currently reading

Published by Oxford University Press in Oxford, New York .
Written in English

    Subjects:
  • Yang-Baxter equation,
  • Representations of groups,
  • Quantum groups

  • Edition Notes

    Includes bibliographical references and index.

    StatementPavel Etingof and Frédéric Latour.
    SeriesOxford lecture series in mathematics and its applications ;, 29
    ContributionsLatour, Frédéric.
    Classifications
    LC ClassificationsQC174.52.Y36 E85 2005
    The Physical Object
    Paginationxi, 138 p. :
    Number of Pages138
    ID Numbers
    Open LibraryOL3436392M
    ISBN 100198530684
    LC Control Number2005280920
    OCLC/WorldCa56654743

    A detailed analysis of the constant quantum Yang–Baxter equation R k 1 k 2 j 1 j 2 R l 1 k 3 k 1 j 3 R l 2 l 3 k 2 k 3 = R k 2 k 3 j 2 j 3 R k 1 l 3 j 1 k 3 R l 1 l 2 k 1 k 2 in two dimensions is presented, leading to an exhaustive list of its solutions. The set of 64 equations for 16 unknowns was first reduced by hand to several subcases which were then solved by computer using the Gröbner. Dynamical Yang-Baxter Maps Associated with Homogeneous Pre-Systems Kamiya, Noriaki and Shibukawa, Youichi, Journal of Generalized Lie Theory and Applications, ; Affine actions and the Yang–Baxter equation Yang, Dilian, Advances in Operator Theory, ; A characterization of finite multipermutation solutions of the Yang–Baxter equation Bachiller, D., Cedó, F., and Vendramin, L.

    Classical and quantum dynamical Yang-Baxter equation. J.-L. Gervais, A. Neveu, Novel triangle relation and absence of tachyons in Liouville string field theory, Nuclear Phys. B (), no. 1, –, MR86f, doi. 4. Quantum groups 5. Intertwiners, fusion and exchange operators for UULq (g) 6. Dynamical R-matrices and integrable systems 7. Traces of intertwiners for UULq (g) 8. Traces of intertwiners and Macdonald polynomials 9. Dynamical Weyl group.

    The Yang-Baxter-Zamolodchikov-Faddeev (YBZF) algebras and their many applications are the subject of this reivew. I start by the solvable lattice statistical models constructed from YBZF algebras. All two-dimensional integrable vertex models follow in this way and are . Since then, the theory of dynamical Yang-Baxter equations and the corresponding quantum groups was systematically developed in many papers. By now, this theory has many applications, in particular to integrable systems and representation theory. The goal of this paper is to discuss this theory and some of its t: 39 pages.


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The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems by P. I. Etingof Download PDF EPUB FB2

The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable And quantum integrable systems book Pavel Etingof, Frederic Latour The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and.

It is ideal for a graduate course on quantum grounps and special functions. Mathematical Reviews This monograph provides an excellent introduction to the theory of the quantum dynamical Yang-Baxter equation from th point of view of (quantum) integrable systems and special function theory.

Mathematical ReviewsCited by: Get this from a library. The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems.

[P I Etingof; Frédéric Latour] -- "This text, based on an established graduate course given at MIT, provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in.

The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems. [P I Etingof; Frédéric Latour] -- The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in.

The ABRR equation for iiq(0) 64 Quasi-classical limit for ABRR equation for ilq (g) 65 Dynamical R-matrices and integrable systems 70 Classical mechanics vs. quantum mechanics 70 Transfer matrix construction 71 Dynamical transfer. The QDYB equation and its quasiclassical analogue (the classical dynamical Yang–Baxter equation) arise in several areas of mathematics and mathematical physics (conformal field theory, integrable systems, representation theory).

The most interesting solution of the QDYB equation is the elliptic solution, discovered and quantum integrable systems book Felder. Since then, the theory of dynamical Yang-Baxter equations and the corresponding quantum groups was systematically developed in many papers.

By now, this theory has many applications, in particular to integrable systems and representation theory. Abstract: The quantum dynamical Yang-Baxter (QDYB) equation is a useful generalization of the quantum Yang-Baxter (QYB) equation introduced by Gervais, Neveu, and Felder.

The QDYB equation and its quasiclassical analogue (the classical dynamical Yang-Baxter equation) arise in several areas of mathematics and mathematical physics (conformal field theory, integrable systems, representation theory).

The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems. Oxford Lecture Series in Mathematics and its Applications, Oxford University Press, Oxford, xii+ pp. ISBN: ; MR (k)] $\endgroup$ – Leandro Vendramin Apr 4 '15 at Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation.

The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of.

Quantum groups and Lie theory / edited by Andrew Pressley. Show more Show less. Integrable and Weyl modules for quantum affine sl₂ / Vyjayanthi Chari & Andrew Pressley -- Notes on balanced categories and Hopf algebras / Bernhard Drabant -- Lectures on the dynamical Yang-Baxter equations / Pavel Etinghof & Olivier Schiffmann -- Quantized.

Plus contributions which treat the construction and classification of quantum groups or the associated solutions of the quantum Yang-Baxter equation. The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of.

to the quantum Yang-Baxter equation. Following a similar procedure, fusion opera-tors are used to de ne exchange operators or quantum dynamical R -matrices that are solutions to the quantum dynamical Yang-Baxter equation.

The quantum dynamical R -matrices are used to construct a set of transfer operators that describe a quantum in-tegrable system.

This quantum equation is called the quantum dynamical Yang-Baxter equation (QDYBE). It was rst intro-duced by Gervais and Neveu [GN] and later by Felder [F1], as a quantization of (5).

This equation has important applications in the theory of integrable systems [ABB]. QDYBE is a generalization of the usual quantum Yang-Baxter equation, and it. P.R. SETHNA, in International Symposium on Nonlinear Differential Equations and Nonlinear Mechanics, Introduction. Vibrations of dynamical systems of multiple-degrees of freedom for motions in the neighborhood of stable static equilibrium have been studied for a long time.

In the classical theory [7] the analysis is restricted to values of the coordinates in the immediate neighborhood of. A brief introduction is given to the Yang-Baxter equation in integrable quantum field theory and lattice statistical physics.

The quantum group is primarily introduced as a systematic method for. Etingof and F. Latour, The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems, vol.

29 of Oxford Lecture Series in Mathematics and Its Applications, Oxford University Press, Oxford, System Upgrade on Fri, Jun 26th, at 5pm (ET) During this period, our website will be offline for less than an hour but the E-commerce and registration of new users may not be available for up to 4 hours.

For online purchase, please visit us again. Contact us at [email protected] for any enquiries. We derive new holonomicq-difference equations for the matrix coefficients of the products of intertwining operators for quantum affine algebra representations of levelk.

We study the connection opertors between the solutions with different asymptotics and show that. Here we introduce a (1 + 1)-dimensional integrable quantum evolution system with discrete space and time. In doing this we follow the scheme suggested in, and further developed in.

Remind that the quantum Yang–Baxter map acts on a tensor square of the algebra A, () R: (A 1 ⊗ A 2) ↦ (A 1 ′ ⊗ A 2 ′) = R (A 1 ⊗ A 2) R − 1. In the context of differential equations to integrate an equation means to solve it from initial ingly, an integrable system is a system of differential equations whose behavior is determined by initial conditions and which can be integrated from those initial conditions.

Many systems of differential equations arising in physics are integrable.E. Ragoucy's research works with 1, citations and 2, reads, including: Classical W-algebras for Centralizers.The tetrahedron equation is a three-dimensional generalization of the Yang-Baxter equation.

Its solutions define integrable three-dimensional lattice models of statistical mechanics and quantum field theory.