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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Family of Affine Quantum Group Invariant Integrable Extensions of Hubbard Hamiltonian
TL;DR: The spin chain Hamiltonians of as mentioned in this paper have affine quantum group symmetry and have the degeneracy of levels, corresponding to affine QG. But their eigenvalues coincide with those of the usual spin chains, but have different degeneracy.
Journal ArticleDOI
Deformed boson algebras and the quantum double construction
D. S. McAnally,I Tsohantjis +1 more
TL;DR: In this article, the quantum double construction of a q-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly and the R-matrix is compared with the existing literature.
Journal ArticleDOI
A geometric Schur-Weyl duality for quotients of affine Hecke algebras
TL;DR: In this article, a geometric Schur-Weyl duality for quotients of affine Hecke algebras was established in type A in the finite and affine case.
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Quantum group Uq(Dℓ) singular vectors in the Poincaré-Birkhoff-Witt basis
TL;DR: The authors give explicit expressions for the singular vectors of Uq(Dl) in terms of the Poincare-Birkhoff-Witt basis and relate these expressions to those of simple root vectors.
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Evaluation representations of quantum affine algebras at roots of unity
Yuuki Abe,Toshiki Nakashima +1 more
TL;DR: In this article, the authors compute the Drinfel polynomials for two types of evaluation representations of quantum affine algebras at roots of unity and construct those representations as the submodules of evaluation Schnizer modules.
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.
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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.