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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Quantum supergroup structure of (1+1)-dimensional quantum superplane, its dual and its differential calculus
M. El Falaki,E. H. Tahri +1 more
TL;DR: In this article, it was shown that the (1+1)-dimensional quantum superplane introduced by Manin is a quantum supergroup, according to the Faddeev-Reshetikhin-Takhtajan approach, when it is extended by the inverse of the bosonic variable.
Journal ArticleDOI
The -schur algebras and -schur dualities of finite type
Li Luo,Weiqiang Wang +1 more
TL;DR: In this paper, a simple Lie algebra with Weyl group (W$)-invariant finite set of integral weights is constructed for the class of classes of algebraic types and a duality between the Schur algebra and Hecke algebra is established.
Journal ArticleDOI
Marumori expansion for a single j-shell within the quon algebra
Sidney S. Avancini,F. F. de Souza Cruz,J. R. Marinelli,D. P. Menezes,M. M. Watanabe de Moraes +4 more
TL;DR: In this paper, the quon algebra is used to generate deformed Marumori boson expansions for the pair and quadrupole operators, which are then used to obtain a pairing plus quadrupelle-quadrupole Hamiltonian for a single j-shell, in terms of these deformed operators.
Journal ArticleDOI
Set-theoretic Yang–Baxter & reflection equations and quantum group symmetries
TL;DR: In this article, the connection between set-theoretic Yang-Baxter and reflection equations and quantum integrable systems is investigated, and the corresponding defining algebra relations for R-matrices being Baxterized solutions of the A-type Hecke algebra are derived.
Posted Content
A Partition Temperley-Lieb Algebra
TL;DR: In this paper, a generalization of the Temperley-Lieb algebra is defined by adding certain relations to the algebra of braids and ties, which corresponds to one small Ramified Partition algebra, this fact is the motivation for the name of their generalization.
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.