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
Category of nonlinear evolution equations, algebraic structure, and r-matrix
TL;DR: In this paper, the category of nonlinear evolution equations (NLEEs) associated with the spectral problem is introduced and an approach for constructing their algebraic structure and r-matrix is provided.
Journal ArticleDOI
Affine flag varieties and quantum symmetric pairs
TL;DR: In this paper, the quantum groups arising from Lusztig algebras and Schur algesbras via stabilization procedures were shown to be (idempotented) co-algebra of quantum groups of affine groups of finite and affine types.
Journal ArticleDOI
The Universal R Matrix for U($q$) Sl(3) and Beyond!
TL;DR: In this paper, the R-matrices for the quantised Lie algebrasAn are constructed through the quantum double procedure given by Drinfel'd [6], and the case of Uqsl(3) is thoroughly analysed initially to demonstrate the more subtle points of the calculation.
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Level-rank duality in quantum groups
Hubert Saleur,D. Altschüler +1 more
TL;DR: In this paper, the commutant of U q sl(n) in Y nk ⊗ L and the corresponding commutants in 1 Y kn ⊆ L (where Y is a young tableau and 1 Y its transpose with respect to NW-SE diagonal) are mapped onto each other by R nk → R kn −1.
Journal ArticleDOI
Dynamical Properties of a Two-Level Atom in Three Variants of the Two-Photon q-Deformed Jaynes–Cummings Model
TL;DR: Temporal evolution of atomic properties including population inversion and quantum fluctuations of atomic dipole variables are discussed in three variants of the two-photon q-deformed Jaynes-C... as mentioned in this paper.
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.