Journal ArticleDOI
A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation
TLDR
In this article, the structure and representations of the universal enveloping algebra U(g) were studied for g = g[(N+1) the structure of the algebra Ŭ(g), a q-analogue of the Universal Enveloping Algebra (U(g)).Abstract:
We study for g=g[(N+1) the structure and representations of the algebra Ŭ(g), a q-analogue of the universal enveloping algebra U(g). Applying the result, we construct trigonometric solutions of the Yang-Baxter equation associated with higher representations of g.read more
Citations
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Journal ArticleDOI
Introduction to Quantum Integrability
TL;DR: In this article, the basic concepts regarding quantum integrability are reviewed and a short review on quantum groups as well as the quantum inverse scattering method (algebraic Bethe ansatz) is also presented.
Journal ArticleDOI
A realization of the q-deformed harmonic oscillator: rogers-Szegö and Stieltjes-Wigert polynomials
TL;DR: In this article, the authors discuss some results from q-series that can account for the foundations for the introduction of orthogonal polynomials on the circle and on the line.
Journal ArticleDOI
Effect of the Wigner-Dunkl algebra on the Dirac equation and Dirac harmonic oscillator
TL;DR: In this paper, the Dirac equation and Dirac harmonic oscillator in one-dimensional via the Dunkl algebra were solved by using Dunkl derivative and the momentum operator and Hamiltonian.
Book ChapterDOI
Quantum Groups and q-Orthogonal Polynomials
TL;DR: In this paper, the authors give a survey on recent works concerning the realization of q-analogues of the Jacobi polynomials as spherical functions on the quantum group SU.
Journal ArticleDOI
A deformation of quantum mechanics
You-quan Li,Zheng-Mao Sheng +1 more
TL;DR: In this paper, the Hermitian conjugation of a q-differential operator is discussed on a one-dimensional lattice without uniform interval, and a deformation of quantum mechanics in one dimension is presented.
References
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Book
Groupes et algèbres de Lie
TL;DR: Les Elements de mathematique de Nicolas Bourbaki ont pour objet une presentation rigoureuse, systematique et sans prerequis des mathematiques depuis leurs fondements as mentioned in this paper.
Journal ArticleDOI
A q -difference analogue of U(g) and the Yang-Baxter equation
TL;DR: Aq-difference analogue of the universal enveloping algebra U(g) of a simple Lie algebra g is introduced in this article, and its structure and representations are studied in the simplest case g=sl(2).
Journal ArticleDOI
Some Exact Results for the Many-Body Problem in one Dimension with Repulsive Delta-Function Interaction
TL;DR: In this paper, the ground-state problem of spin-textonehalf{} fermions is reduced to a generalized Fredholm equation, in a generalized form, by using Bethe's hypothesis.
Journal ArticleDOI
Yang-baxter equation and representation theory: i
TL;DR: In this article, the problem of constructing the GL(N,ℂ) solutions to the Yang-Baxter equation (factorizedS-matrices) is considered.