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
The Quantum Double in Integrable Quantum Field Theory
Denis Bernard,André LeClair +1 more
TL;DR: In this article, a geometrical meaning is given to the quantum double and other properties of quantum groups, and a multiplicative presentation of the Yangian double is analyzed in the context of 2D quantum field theory.
Journal ArticleDOI
Solutions of the Quantum Yang-Baxter Equation with Extra Nonadditive Parameters
TL;DR: In this article, a spectral-dependent solution to the Yang-Baxter equation is presented, which depends not only on a spectral parameter, but also on further continuous parameters such as the spectral parameter in a non-additive form.
Journal ArticleDOI
Quantum (2+1) kinematical algebras: a global approach
TL;DR: In this article, the authors give an approach to quantum deformations of the (2+1) kinematical Lie algebras within a scheme that simultaneously describes all groups of motions of classical geometries in N = 3 dimensions.
Journal ArticleDOI
Matrix units for centralizer algebras
Arun Ram,Hans Wenzl +1 more
TL;DR: In this paper, a complete system of matrix units of the centralizers of tensor products of classical Lie groups (except SO(2n)) and their quantum deformations 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.
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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.