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
Dynamics of a Q-analogue of the Quantum Harmonic Oscillator
TL;DR: In this paper, the dynamics of the q-deformed quantum harmonic oscillator initially prepared in the qanalogue of the coherent state is analyzed. And the squeezing of the second-order moments of this operator is studied.
Journal ArticleDOI
Restricted limits of minimal affinizations
TL;DR: In this article, character formulas of minimal affinizations of representations of quantum groups were obtained for the case that the underlying simple Lie algebra is orthogonal and the support of the highest weight is contained in the first three nodes of the Dynkin diagram.
Book ChapterDOI
Multiplicative Slices, Relativistic Toda and Shifted Quantum Affine Algebras
TL;DR: In this paper, the shifted quantum affine algebras are introduced, which map homomorphically into the quantized K-theoretic Coulomb branches of the SUSY quiver gauge theories.
Journal ArticleDOI
Quantum groups and Lie-admissible time evolution
TL;DR: In this paper, the time evolution of operators for q-oscillators is derived for the first time by exploiting the connection between q-deformation algebras and Lie-admissible alges.
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.