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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Self-Duality for the Two-Component Asymmetric Simple Exclusion Process
TL;DR: In this paper, a two-component asymmetric simple exclusion process (ASEP) with second-class particles was studied and the authors proved self-duality with respect to a family of duality functions which arise from reversible measures of the process and the symmetry of the generator under the quantum algebra.
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Representations of twisted q-Yangians
Lucy Gow,Alexander Molev +1 more
TL;DR: The twisted q-Yangians are coideal subalgebras of the quantum affine algebra associated with gl(N) as discussed by the authors, and they are parameterized by their highest weights or by their Drinfeld polynomials.
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$(q,t)$-KZ equations for quantum toroidal algebra and Nekrasov partition functions on ALE spaces
Hidetoshi Awata,Hiroaki Kanno,Andrei Mironov,Alexei Morozov,Alexei Morozov,Kazuma Suetake,Yegor Zenkevich,Yegor Zenkevich,Yegor Zenkevich +8 more
TL;DR: In this paper, the Wess-Zumino-Witten model was lifted from the level of one-loop Kac-Moody to generic quantum toroidal algebras.
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Finite-dimensional singletons of the quantum anti de sitter algebra
V. K. Dobrev,Patrick Moylan +1 more
TL;DR: In this paper, positive energy irreducible representations of the q -deformed anti de Sitter algebra U q (so(3,2)) by deformation of the classical ones were obtained.
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Brundan-Kazhdan-Lusztig and super duality conjectures
Shun-Jen Cheng,Weiqiang Wang +1 more
TL;DR: In this paper, a super duality conjecture on connections between parabolic categories O of modules over Lie superalgebras and Lie algebra of type A, based on a Fock space formalism of their Kazhdan-Lusztig theories, was formulated.
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.