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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On the Quantum Group SLq(2)
Joseph Bernstein,Tanya Khovanova +1 more
TL;DR: In this paper, a general method of constructing quantum groups with similar properties was developed in the language of quantized universal enveloping algebras, which is another common method of studying quantum groups.
Dissertation
Approaches to form-factors of higher spin Heisenberg chains
TL;DR: In this paper, the vertex operator approach was applied to higher spin Heisenberg chains with the aim of computing the formfactors of these quantum integrable models, motivated by the relation of the form-factors to the dynamical structure factors of the model objects that are experimentally realisable and potential for comparison with real-world results.
Posted Content
Hecke algebras, $U_qsl_n$, and the Donald--Flanigan conjecture for $S_n$
Murray Gerstenhaber,Mary Schaps +1 more
TL;DR: In this article, the authors show that the Hecke algebra of a simple module with an orthogonal basis indexed by Young diagrams is a global solution to the Donald-Flanigan problem for the quantized case.
Journal ArticleDOI
Models solvable by Bethe Ansatz 1
TL;DR: In this paper, the Schur-Weyl duality between sl2 and the symmetric group SN was extended to a general spin chain related to the Temperley-Lieb algebra TLN(q) and a new quantum algebra Uq(n) with the representation ring equivalent to the sl2 one.
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.