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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New reflection matrices for the U_q(gl(m|n)) case
Anastasia Doikou,Nikos Karaiskos +1 more
TL;DR: In this paper, super symmetric representations of the B-type Hecke algebra were obtained for the boundary super algebra U_q(gl(m|n) n).
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The Robinson---Schensted correspondence and $$A_2$$A2-web bases
TL;DR: In this paper, the authors study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to $$[n, n,n,n]$$[n, n, n,n] : the reduced web basis associated to Kuperberg's combinatorial description of the spider category; and the left cell basis for the left-cell construction of Kazhdan and Lusztig.
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Raising/Lowering Maps and Modules for the Quantum Affine Algebra
TL;DR: In this paper, the authors show that there exists a unique -module structure on V such that each of,, K −− K 0, and K −1−K 1 vanish on V, where are Chevalley generators for.
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The Robinson-Schensted correspondence as the quantum straightening at $q=0$
Bernard Leclerc,Jean-Yves Thibon +1 more
TL;DR: It is shown that the quantum straightening algorithm for Young tableaux and Young bitableaux reduces in the crystal limit to the Robinson-Schensted algorithm.
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Regular XXZ bethe states at roots of unity as highest weight vectors of the sl2 loop algebra
TL;DR: In this paper, it was shown that every regular Bethe ansatz eigenvector of the XXZ spin chain at roots of unity is the highest weight vector of the sl2 loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator SZ.
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).
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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.