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
Oscillator versus prefundamental representations
TL;DR: For the case of quantum loop algebras, the authors obtained the weights and weight vectors for the representations obtained via Jimbo's homomorphism, known also as evaluation representations.
Journal ArticleDOI
Lefschetz property, Schur-Weyl duality and a q-deformation of Specht polynomial
TL;DR: In this article, the Schur-Weyl duality for a polynomial representation of the quantum group and the Hecke algebra of type A was described from a viewpoint of a q-analog of the strong Lefschetz property.
Journal ArticleDOI
Quantum Groups as Hidden Symmetries of Quantum Impurities.
TL;DR: The approach based on quantum groups does not only allow for a drastic simplification of impurity problems, but also provides valuable insights into hidden symmetries of interacting many-particle systems.
Book ChapterDOI
Twist Deformations of Quantum Integrable Spin Chains
TL;DR: In this paper, it is shown that the spectrum of the XXX spin chain is preserved under the twist deformation while the structure of the eigenstates depends on the choice of boundary conditions.
Journal ArticleDOI
Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model
Nenad Manojlovic,Igor Salom +1 more
TL;DR: In this paper, the implementation of algebraic Bethe ansatz for the XXZ Heisenberg spin chain in the case, when both reflection matrices have the upper-triangular form is analyzed.
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.