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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The Integral on Quantum Super Groups of Type $A_{r|s}$
TL;DR: In this paper, the integral on matrix quantum groups of type $A r|s$ and derive from it the quantum analogue of (super) HCIZ integral are derived. But they do not consider quantum groups.
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On the quantum super Virasoro algebra
TL;DR: In this article, the quantum super-algebra structure on the deformed super Virasoro algebra is investigated, and the possibility of defining a non trivial Hopf superalgebra on both one and two-parameters deformed SV algebras is established.
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Quantum Schur–Weyl duality and projected canonical bases
TL;DR: In this article, it was shown that the transition matrix S(λ) between the two Kazhdan-Lusztig bases is the identity at u=0 and u=∞.
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On $q$-Deformed Spinning Relativistic Particle
TL;DR: In this paper, a q-deformed free spinning relativistic particle is discussed in the framework of the Lagrangian formalism, and three equivalent Lagrangians are obtained for this system which are endowed with q-formed local (super) gauge symmetries and reparametrization invariance.
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A central extension of U_q sl(2,2)^{(1)} and R-matrices with a new parameter
TL;DR: In this paper, a quantum superalgebra associated with the universal central extension of U_q sl(2,2)^{(1)} was introduced, and new R-matrices having an extra parameter x were introduced.
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.
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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.