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
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$R$ matrix for generalized quantum group of type $A$
Jae-Hoon Kwon,Jeongwoo Yu +1 more
TL;DR: The generalized quantum group of type $A$ is an affine analogue of quantum group associated to a general linear Lie superalgebra as mentioned in this paper, and it is shown that there exists a unique $R$ matrix on tensor product of fundamental type representations of $\mathcal{U}(\epsilon)$ for arbitrary parameter sequence corresponding to a nonconjugate Borel subalgebra.
Journal ArticleDOI
Derived equivalences and sl2-categorifications for Uq(gln)
TL;DR: In this paper, a construction of sl 2 -categorifications for U q (gl n ), for generic q and for q a root of unity is given, based on the concept of unity root.
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The $q-$Onsager algebra and multivariable $q-$special functions
TL;DR: In this paper, two sets of mutually commuting $q-$difference operators are introduced, such that the action of each operator with respect to its dual basis is block tridiagonal and the overlap coefficients between the two dual bases are expressed as entangled products of $q-Racah polynomials and satisfy an orthogonality relation.
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Invariants of the quantum supergroup Uq(gl(m/1))
TL;DR: In this article, a spectral parameter dependent solution of the graded Yang-Baxter equation is obtained, which in Uq(gl(m/1))(X)End(V) with V being the vector module of Uq (gl m/1) is constructed using a general method developed in an earlier publication.
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Molecular Spectra from Rotationally Invariant Hamiltonians Based on the Quantum Algebra SUq(2) and Irreducible Tensor Operators under SUq(2)
TL;DR: In this paper, the rotational invariance of the SUq(2) ITO Hamiltonian for the description of rotational molecular spectra is explicitly proved and a connection of this Hamiltonian to the formalism of Amal'sky is provided.
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).
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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.