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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Journal ArticleDOI
A solution to quantum Knizhnik-Zamolodchikov equations and its application to eigenvalue problems of the Macdonald type
Journal ArticleDOI
Quantum group symmetries in two-dimensional lattice quantum field theory
Denis Bernard,Giovanni Felder +1 more
TL;DR: In this paper, a general theory of non-local conserved currents in two-dimensional quantum field theory in the lattice approximation is presented, which reflect quantum group symmetries.
Journal ArticleDOI
A Duality Theorem for Ergodic Actions of Compact Quantum Groups on C*-Algebras
Claudia Pinzari,John E. Roberts +1 more
TL;DR: The spectral functor of an ergodic action of a compact quantum group on a unital C*-algebra is quasitensor, in the sense that the tensor product of two spectral subspaces is isometrically contained in the spectral subspace of the representation, and the inclusion maps satisfy natural properties.
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Subsingular vectors and conditionally invariant (q-deformed) equations
TL;DR: In this article, the relation between subsingular vectors of Verma modules over semisimple Lie algebras G and differential equations which are conditionally G-invariant is discussed.
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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 the symplectic Lie algebra as discussed by the authors, which are parameterized by their highest weights satisfying certain dominance-type conditions.
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.