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 central extension of the reflection equations and an analog of Miki’s formula
Pascal Baseilhac,Samuel Belliard +1 more
TL;DR: In this paper, two different types of centrally extended quantum reflection algebras are introduced and a co-action map is identified for the special case of, a realization in terms of elements satisfying the Zamolodchikov-Faddeev algebra is proposed, providing a free-field realization of q-Onsager currents.
Book ChapterDOI
From Integrable Models to Quantum Groups
TL;DR: In this article, a purely algebraic synthesis of the technical developments in mathematical physics is found, where the history of quantum groups is quite exciting and instructive, and a notion of quantum group is introduced.
Journal ArticleDOI
Generalized commutators and deformation of strong coupling superconductivity
Wei-Yeu Chen,Choon-Lin Ho +1 more
TL;DR: In this article, the authors considered quantum deformation of a strong-coupling superconductivity model based on creation/annihilation operators which satisfy generalized commutator relations and showed that the nature of the superconducting phase transition can be changed from the usual second-order to a first-order transition if the deformation parameter exceeds a certain critical value.
Journal ArticleDOI
Hecke algebras, _{}_{}, and the Donald-Flanigan conjecture for _{}
Murray Gerstenhaber,Mary Schaps +1 more
TL;DR: In this article, it was shown that the Hecke algebra of S n is a global solution to the Donald-Flanigan problem for S n. The main result of this paper is a new demonstration of the relation between (nonincreasing) partitions p of n and representations of the symmetric group S n, which carries over immediately to the quantized case.
Journal ArticleDOI
A Q-operator for open spin chains I. Baxter's TQ relation
Bart Vlaar,Robert Weston +1 more
TL;DR: In this paper, a Q-operator for the open XXZ Heisenberg quantum spin chain with diagonal boundary conditions was constructed and a rigorous derivation of Baxter's TQ relation was given.
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.