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
Fusion Formulas and Fusion Procedure for the Yang-Baxter Equation
TL;DR: In this article, the authors used the fusion formulas of the symmetric group and of the Hecke algebra to construct solutions of the Yang-Baxter equation on irreducible representations.
Journal ArticleDOI
Quantum deformation of the U(4) supset SO(4) supset SO(3) chain and the description of rotation-vibration spectra of diatomic molecules
TL;DR: In this article, the deformation of the U(4) supset SOq(4), SOq'(4)-supset Soq' (3) algebra chain was studied and the results showed that the six-parameter formula obtained from the U((4, SOq, 4) + SOq) algebraic chain can be used to sum up the Dunham expansion fully.
Posted Content
Stable maps, Q-operators and category O
TL;DR: In this paper, the authors define and construct stable maps on tensor products of representations in the category O of the Borel subalgebra of an arbitrary untwisted quantum affine algebra.
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Iterative construction of $U_q (s\ell (n+1)) $ representations and Lax matrix factorisation
TL;DR: In this paper, the construction of a generic representation of $g\ell(n+1)$ or of the trigonomentric deformation of its enveloping algebra known as algebraic induction is conveniently formulated in term of Lax matrices.
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On the elliptic 2 solid-on-solid model: Functional relations and determinants
TL;DR: In this article, the authors studied an elliptic solid-on-solid model with domain-wall boundaries having the elliptic quantum group Ep,γ[gl2^] as its underlying symmetry algebra and extended their analysis to include continuous families of single determinantal representations for the model's partition function.
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.
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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).
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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.
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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.