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
More filters
Book ChapterDOI
Linear and Nonlinear Group Actions, and the Newton Institute Program
TL;DR: One of the simplest and most useful notions in mathematics is the notion of group action as mentioned in this paper, which is defined as a multiplication operation of a group action on a nonempty set, with the image of a pair (g, x) written as gx.
Posted Content
The $q$-Schur algebras and $q$-Schur dualities of finite type
Li Luo,Weiqiang Wang +1 more
TL;DR: In this article, a duality between the q-Schur algebra and Hecke algebra associated to a simple Lie algebra with Weyl group was established, and a canonical basis for the q -Schur algebras with positivity was constructed.
Journal ArticleDOI
A central extension of Uq sl(2|2)(1) and R-matrices with a new parameter
TL;DR: In this paper, a quantum superalgebra associated with the universal central extension of sl(2|2)(1) was used to construct new R-matrices having an extra parameter x.
Book ChapterDOI
Fluctuations in Stochastic Interacting Particle Systems II
TL;DR: In this paper, the authors discuss fluctuations in stochastic lattice gas models from a microscopic and mesoscopic perspective by using techniques from algebra, in particular the use of symmetries and time-reversal.
Journal ArticleDOI
Universal R-matrix and functional relations
TL;DR: In this paper, general definitions and facts on the application of quantum groups to the construction of functional relations in the theory of integrable systems are collected and systematize general definition and facts.
References
More filters
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.