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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Positive Line Bundles Over the Irreducible Quantum Flag Manifolds
TL;DR: In this article, a non-commutative Borel-Weil theorem for positive line bundles of irreducible quantum flag manifolds is introduced, which is a generalisation of the Bott-Borel Weil theorem.
Journal ArticleDOI
Contracted and expanded integrable structures
TL;DR: In this article, the authors propose a generic framework to obtain certain types of contracted and centrally extended algebras, which are associated to rational and trigonometric R-matrices that are solutions of the Yang-Baxter equation.
Journal ArticleDOI
New reflection matrices for the Uq(gl(m|n)) case
Anastasia Doikou,Nikos Karaiskos +1 more
TL;DR: In this article, supersymmetric representations of the B-type Hecke algebra are examined and the boundary super algebra is shown to be central to the supersymmetric realization of the super algebra.
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q-deformed SUSY algebra for a ?-covariant q-boson and q-fermion system
TL;DR: The q-deformed N = 2 SUSY algebra for a -covariant q-boson and q-fermion system was obtained in this paper.
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Quantum toroidal algebras and their representations
TL;DR: In this paper, a review of double affine quantum algebras is presented, with a glimpse on some aspects of their representation theory in the context of general quantum affinizations.
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.