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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Distinguished Pre-Nichols algebras
TL;DR: In this paper, the distinguished pre-Nichols algebra of a braided vector space of diagonal type with finite-dimensional Nichols algebra is defined and studied, which is intermediate between the tensor algebra $T(V)$ and the Nichols algebra of the vector space.
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Harmonic Oscillator Realization of the Deformed Bogoliubov (p,q)- Transformations without First Finite Fock States
TL;DR: In this paper, a new harmonic oscillator realization of the deformed boson operators based on the Bogoliubov (p, q)-transformations is presented. But the transformation coefficients depend on arbitrary functions of p and q which can be interpreted as the parameters of the (p and q)-deformed GL(2,C) group.
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Canonical bases for modified quantum gln and q-Schur algebras
TL;DR: In this article, an elementary algebraic construction of canonical bases for modified quantum gln and q-Schur algebras is presented, and the relation between the canonical basis of the positive part of the q-schur algebra and the canonical base of modified gln is discussed.
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A physical interpretation of the quantum group Uq(SU(2))
TL;DR: In this paper, the quantum statistics of a system of free spins in the presence of a constant magnetic field H is interpreted in terms of the representation theory of the simplest quantum group Uq(SU(2)) with q=e( mu 0 mu BkBT)/ being the deformation parameter which has a definite physical meaning.
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Shell correlations in the SUq(2) rotor model
TL;DR: In this paper, an analytical correlation between the quantum algebraic parameter tau and the number of nucleon pairs in the valence shells N is established, and it is shown that such a correlation actually applies in rotational regions 150 220 and justifies the physical interpretation of tau in connection with nuclear softness.
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.