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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Quantum groups and fusion rules multiplicities
TL;DR: In this article, a truncation of the tensor product of two regular representations of Uq(g) for q a root of unity is performed, and it coincides with the fusion rules for integrable representations in a WZW theory based on the affine Lie algebra g(1).
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PT symmetry on the lattice: the quantum group invariant XXZ spin chain
Christian Korff,Robert Weston +1 more
TL;DR: The PT-symmetry of the quantum group invariant XXZ chain was investigated in this paper, where it was shown that the PT operator commutes with quantum group action and also discussed the transformation properties of the Bethe wavefunction.
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Integrability for multidimensional lattice models
TL;DR: In this article, the generating principle for the algebraic construction of the hierarchy of the d-simplex equations generalizing the Yang-Baxter equation in any dimension d is given.
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Exercises with the universal R-matrix
Herman Boos,Frank Göhmann,Andreas Klümper,Khazret S. Nirov,Khazret S. Nirov,Alexander V. Razumov +5 more
TL;DR: Using the formula for the universal R-matrix proposed by Khoroshkin and Tolstoy, this article gave a detailed derivation of L-operators for the quantum groups associated with the generalized Cartan matrices A(1)1 and A( 1)2.
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Quantum deformations of SU(2)
TL;DR: In this article, explicit representations of two deformations of SU(2), one in the Cartan basis, and one in Cartesian basis, are constructed, and explicit reversible mappings in terms of representations of SU (2) and a Casimir for the algebra are constructed.
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.