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
Wigner-Eckart theorem for the quantum group Uq(n)
TL;DR: In this article, tensor operators transforming under finite dimensional irreducible representations of the quantum group Uq(n) are defined. And the Wigner-Eckart theorem on matrix elements of tensor operator defined is derived.
Journal ArticleDOI
Non-standard R-matrices for the Yang—Baxter equation and boson representations of the quantum algebra Slq(2) with qP= ±1*
TL;DR: By constructing a new q-deformed boson realization of the quantum universal enveloping algebra sl q (2) its finite dimensional representations with an arbitrary parameter are obtained in the case that q is a root of unity as discussed by the authors.
Journal ArticleDOI
Grothendieck Groups of a Class of Quantum Doubles
TL;DR: In this paper, an n4-dimensional Hopf algebra Hn(p,q) was constructed, which is isomorphic to D(An(ω)) if p ≠ 0 and q = ω-1.
Journal ArticleDOI
Irreducible representations of Hecke algebras in the nonstandard basis and subduction coefficients
Feng Pan,Jin-Quan Chen +1 more
TL;DR: In this paper, the transformation coefficients between the standard and nonstandard base of Hecke algebras of the type An-1, Hn(q) were derived by using the linear equation method.
Dissertation
Fluctuations quantiques de la signature de la metrique a l'echelle de planck
TL;DR: In this article, the authors propose a construction of a "chemin de fluctuation" (3, 1)-(4, 0) excluant the signature ultra-hyperbolique (2, 2) of Lorentzienne and Euclidienne.
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.