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
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CSOS models descending from chiral Potts models: degeneracy of the eigenspace and loop algebra
Helen Au-Yang,Jacques H. H. Perk +1 more
TL;DR: In this paper, the existence of quantum loop algebra in CSOS models is established by showing that the Serre relations hold for the generators of the generators and the highest weight polynomial of the representation is obtained by using the method of Baxter for the superintegrable case.
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Boson realization of non-generic sLq(2)-R matrices for the Yang-Baxter equation
TL;DR: In this article, a new boson realization of quantum universal enveloping algebra slq(2) and its representations in the non-generic case that q is a root of unity were constructed.
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Quantum superalgebras at roots of unity and topological invariants of three-manifolds
TL;DR: In this paper, a topological invariant of closed, connected, orientable 3-manifolds from a new class of algebras called pseudo-modular hopf algesbras is developed.
Journal ArticleDOI
On the quantum super Virasoro algebra
TL;DR: In this paper, the quantum super-algebra structure on the deformed super Virasoro algebra is investigated, and the possibility of defining a nontrivial Hopf superalgebra on both one and two-parameters deformed SV algebras is established.
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Temperley-Lieb, Birman-Murakami-Wenzl and Askey-Wilson algebras and other centralizers of $U_q(\mathfrak{sl}_2)$.
TL;DR: In this article, the centralizer of the image of the diagonal embedding of U_q(mathfrak{sl}_2) in the tensor product of three irreducible representations is examined in a Schur-Weyl duality spirit.
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.