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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An analogue of P.B.W. theorem and the universalR-matrix forU h sl(N+1)
TL;DR: In this article, an explicit formula for the quantum R-matrix is given for the Poincare-Birkhoff-Witt algorithm. But this formula is based on a quantum double construction.
Journal ArticleDOI
Isomorphism of two realizations of quantum affine algebra\(U_q (\widehat{\mathfrak{g}\mathfrak{l}{\text{(}}n{\text{)}}})\)
Jin Tai Ding,Igor Frenkel +1 more
TL;DR: In this article, an explicit isomorphism between two realizations of the quantum affine algebra was established, which can be considered as an affine version of the isomorphisms between the Drinfield/Jimbo and the Faddeev-Reshetikhin-Semenov-Tian-Shansky constructions.
Journal ArticleDOI
Quantum $\kappa$-Poincare in Any Dimensions
Jerzy Lukierski,Henri Ruegg +1 more
TL;DR: In this article, the quadratic Poisson brackets, determined by the classical $r$-matrix, are calculated, and the quantum Poincar\'e group with noncommuting parameters is obtained.
Journal ArticleDOI
Etiology of IRF models
TL;DR: In this article, a class of 2D statistical mechanics models known as IRF models can be viewed as a subalgebra of the operator algebra of vertex models, and an explicit intertwiner between two representations of this sub-algebra is obtained.
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q-deformed Jacobi identity, q-oscillators and q-deformed infinite-dimensional algebras
TL;DR: In this paper, the general q-deformed Jacobi identity was applied to define relations for q-oscillators and derived the oscillator realization of q -deformed centreless Virasoro.
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).
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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.
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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.