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
Algebraic Aspects of the Quantum Yang-Baxter Equation
L.A. Lambe,David E. Radford +1 more
TL;DR: In this paper, the authors examined a variety of algebraic contexts in which the quantum Yang-Baxter equation arises, and derived methods for generating new solutions from given ones, encoded in objects which have a module and a comodule structure over a bialgebra.
Journal ArticleDOI
On the quantum inverse scattering problem
J. M. Maillet,Véronique Terras +1 more
TL;DR: In this paper, a general method for solving the quantum inverse scattering problem (namely the reconstruction of local quantum operators in term of the quantum monodromy matrix satisfying a Yang-Baxter quadratic algebra governed by an R-matrix) for a large class of lattice quantum integrable models is given.
The history of q-calculus and a new method
TL;DR: In this paper, the authors considered the problem of additive number theory for the Riemann surface and showed that the solution of the problem can be expressed as a polynomial series.
Journal ArticleDOI
Quantum groups and subfactors of type $B$, $C$, and $D$
TL;DR: The main object of as mentioned in this paper is the study of a sequence of finite dimensional algebras, depending on 2 parameters, which appear in connection with the Kauffman link invariant and with Drinfeld's and Jimbo's deformation of Lie algesbras of typesB, C and D.
Journal ArticleDOI
Algebraic aspects of increasing subsequences
Jinho Baik,Eric M. Rains +1 more
TL;DR: In this article, a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations are 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.