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
A realization of the quantum Lorentz group
TL;DR: In this article, a realization of a deformed Lorentz algebra is considered and its irreducible representations are found; in the limit $q\to 1$, these are precisely the irreduceible representations of the classical Lorenz group.
Journal ArticleDOI
Many-spinon states and representations of Yangians in the SU(n) Haldane-Shastry model
TL;DR: In this article, the relation of Yangians and spinons in the SU(n) Haldane-Shastry model is studied and the representation theory of the Yangian is shown to be intimately related to the fractional statistics of the spinons.
Journal ArticleDOI
Presenting cyclotomic $q$-Schur algebras
TL;DR: In this article, a presentation of cyclotomic q-Schur algebras by generators and defining relations is given, as well as an algorithm for computing decomposition numbers.
Book ChapterDOI
Integrabile Quantum Mappings and Quantization Aspects of Integrable Discrete-Time Systems
Frank W. Nijhoff,H. W. Capel +1 more
TL;DR: In this paper, a quantum Yang-Baxter structure associated with non-ultralocal lattice models is studied, and the canonical structure of a class of integrable quantum mappings is discussed.
Journal ArticleDOI
Representation and duality of unimodular c * -discrete quantum groups
TL;DR: In this article, the authors consider the case where a continuous action of D on an operator algebra L(H) is defined, and if the inner product on the Hilbert space H is Dinvariant, there is a unique C∗-representation θ of D associated with the action.
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.