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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Transmission matrices in gl N & Uq(gl N ) quantum spin chains
TL;DR: In this paper, the authors considered the quantum spin chains in the presence of integrable spin impurities and derived the associated transmission amplitudes, and corresponding transmission matrices that physically describe the interaction between the various particle-like excitations displayed by these models and the spin impurity.
Journal ArticleDOI
Deformed Poincaré containing the exact Lorentz algebra
TL;DR: In this paper, a deformed Poincare algebra that contains the exact Lorentz algebra is constructed, and the way is paved towards the construction of field theories with improved renormalization propeerties.
Posted Content
On representation theory of quantum $SL_q(2)$ groups at roots of unity
P. Kondratowicz,P. Podles +1 more
TL;DR: In this article, Wang, Wang and Parshall classified the irreducible representations of quantum groups in the case of an odd root of unity, and showed the corresponding representations of universal enveloping algebras of Jimbo and Lusztig.
Journal ArticleDOI
Special functions and infinite-dimensional representations of Lie groups
P. Feinsilver,R. Schott +1 more
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q-deformed Brownian motion
TL;DR: In this article, the notion of q-deformation is carried from the algebra to the domain of stochastic processes, and properties of q -deformed Brownian motion, in particular its nonGaussian nature and cumulant structure, are established.
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.