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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$q$ Deformations of the O(3) Symmetric Spin 1 Heisenberg Chain
TL;DR: In this article, the authors present the general expression for the spin-1 Heisenberg chain invariant under the Uq(SO(3)) quantum algebra, and several physical and mathematical implications are discussed.
Posted Content
Quantum affine algebras and their representations
Vyjayanthi Chari,Andrew Pressley +1 more
TL;DR: In this paper, the authors prove a highest weight theorem classifying finite-dimensional representations of quantum affine algebras and survey what is currently known about the structure of these representations.
Journal ArticleDOI
The algebra of binary search trees
TL;DR: In this article, a monoid structure on the set of binary search trees is introduced, by a process very similar to the construction of the plactic monoid, the Robinson-Schensted insertion being replaced by the binary search tree insertion.
Book
A New Approach to Kazhdan-lusztig Theory of Type $b$ Via Quantum Symmetric Pairs
Huanchen Bao,Weiqiang Wang +1 more
TL;DR: In this article, a new theory of canonical bases arising from quantum symmetric pairs is initiated, which is then applied to formulate and establish a Kazhdan-Lusztig theory for the BGG category O of the ortho-symplectic Lie superalgebras.
Journal Article
PBW-bases of quantum groups.
TL;DR: In this article, the triangul r decomposition U = U~ ® (7° ® t/, see [Ro], was used to obtain related results for the Borel part t/° ® U or even for f/ itself.
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.
Journal ArticleDOI
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.