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
A New Realization of the Quantum Group SU(2) q
TL;DR: In this paper, the Dyson form of the q-deformed boson realization of the quantum group SU(2)q is constructed by means of K-matrix technique.
Journal ArticleDOI
Absence of Cartan subalgebras for right-angled Hecke von Neumann algebras
TL;DR: For a right-angled Coxeter system (W,S) and q>0, it was shown in this article that ℳq is noninjective and has the weak-∗ completely contractive approximation property and the Haagerup property.
Posted Content
Traces of intertwining operators and Macdonald's polynomials
TL;DR: Generalized characters for affine Lie algebras are closely related with so-called correlation functions on the torus in the Wess-Zumino-Witten (WZW) model of conformal field theory as discussed by the authors.
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Gel'fand pair criteria for compact matrix quantum groups
TL;DR: In this article, the authors give Gel'fand-type criteria for compact matrix quantum groups with respect to certain two-sided coideals in the dual of the Hopf ∗-algebra.
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A q‐analog of the quantum central limit theorem for SUq(2)
TL;DR: In this article, it was shown that the limits of the moments and qexponential generating functions for coherent states give for q≳1 (0 < q < 1) the harmonic q−1−oscillator introduced by Biedenharn and Macfarlane.
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).
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.