Yangians and their applications

@inproceedings{Molev2002YangiansAT,
  title={Yangians and their applications},
  author={Alexander I. Molev},
  year={2002}
}
  • A. Molev
  • Published 19 November 2002
  • Mathematics, Physics
Publisher Summary This chapter discusses the Yangians theory and their applications. The discovery of the Yangians is motivated by quantum inverse scattering theory. The Yangians form a remarkable family of quantum groups related to rational solutions of the classical Yang–Baxter equation. For each simple finite-dimensional Lie algebra α over the field of complex numbers, the corresponding Yangian Y (α) is defined as a canonical deformation of the universal enveloping algebra U (α[ x ]) for the… Expand
Coideal subalgebras in quantum affine algebras
We introduce two subalgebras in the type A quantum affine algebra which are coideals with respect to the Hopf algebra structure. In the classical limit q -> 1 each subalgebra specializes to theExpand
Yangians of Lie (super)algebras
This thesis is concerned with extending some well-known results about the Yangians Y (glN) and Y (slN) to the case of super-Yangians. First we produce a new presentation of the Yangian Y (glm|n),Expand
On reflection algebras and twisted Yangians
It is well known that integrable models associated to rational R matrices give rise to certain non-Abelian symmetries known as Yangians. Analogously boundary symmetries arise when general but stillExpand
YANGIANS IN INTEGRABLE FIELD THEORIES, SPIN CHAINS AND GAUGE-STRING DUALITIES
In the following paper, which is based on the author's PhD thesis submitted to Imperial College London, we explore the applicability of Yangian symmetry to various integrable models, in particular,Expand
Quantum Algebras and Integrable Boundaries in AdS/CFT
This thesis studies quantum integrable structures such as Yangians and quantum affine algebras that arise in and are inspired by the AdS/CFT duality, with a primary emphasis on the exploration ofExpand
L∞ - derivations and the argument shift method for deformation quantization algebras
The argument shift method is a well-known method for generating commutative families of functions in Poisson algebras from central elements and a vector field, verifying a special condition withExpand
Casimir Elements for Some Graded Lie Algebras and Superalgebras
We consider a class of Lie algebras L such that L admits a grading by a finite Abelian group so that each nontrivial homogeneous component is one-dimensional. In particular, this class containsExpand
KZ equation, G-opers, quantum Drinfeld–Sokolov reduction, and quantum Cayley–Hamilton identity
The Lax operator of Gaudin-type models is a 1-form at the classical level. In virtue of the quantization scheme proposed by D. Talalaev, it is natural to treat the quantum Lax operator as aExpand
Rational Lax operators and their quantization
We investigate the construction of the quantum commuting hamiltonians for the Gaudin integrable model. We prove that [Tr L^k(z), Tr L^m(u) ]=0, for k,m < 4 . However this naive receipt ofExpand
KZ equation, G-opers and quantum Drinfeld-Sokolov reduction
The Lax operator of the classical Gaudin type models is a 1-form on the classical level. In virtue of the quantization scheme proposed in [Talalaev04] (hep-th/0404153) it is natural to treat theExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 163 REFERENCES
Fundamental representations of Yangians and singularities of R-matrices.
The construction of Ä-matrices is closely related to the representation theory of quantum groups. In particular, there is an important class of quantum groups, called Yangians, such that to everyExpand
Finite dimensional irreducible representations of twisted Yangians
We study quantized enveloping algebras called twisted Yangians. They are analogs of the Yangian Y(gl(N)) for the classical Lie algebras of B, C, and D series. The twisted Yangians are subalgebras inExpand
Yangians and Gelfand-Zetlin Bases
We establish a connection between the modern theory of Yangians and the classical construction of the Gelfand-Zetlin bases for the Lie algebra gln. Our approach allows us to produce the g-analoguesExpand
Yangians and transvector algebras
  • A. Molev
  • Computer Science, Mathematics
  • Discret. Math.
  • 2002
We give a quantum analog of Sylvester's theorem where numerical matrices are replaced with noncommutative matrices whose entries are generators of the Yangian for the general linear Lie algebraExpand
On the Harishchandra homomorphism for infinite-dimensional Lie algebras
A natural generalization of the finite-dimensional semisimple Lie algebras to the infinite-dimensional case is the Kac-Moody Lie algebra G(A) or more generally, the contragredient Lie algebraExpand
NEWTON'S FORMULA FOR GLN
This paper presents an explicit relation between the two sets which are well-known generators of the center of the universal enveloping algebra U(gln) of the Lie algebra gln: one by Capelli (1890)Expand
Yangians, integrable quantum systems and Dorey's rule
It was pointed out by P. Dorey that the three-point couplings between the quantum particles in affine Toda field theories have a remarkable Lie-theoretic interpretation. It is also well known thatExpand
A guide to quantum groups
Introduction 1. Poisson-Lie groups and Lie bialgebras 2. Coboundary Poisson-Lie groups and the classical Yang-Baxter equation 3. Solutions of the classical Yang-Baxter equation 4. QuasitriangularExpand
Sklyanin determinant, Laplace operators, and characteristic identities for classical Lie algebras
The structure of quantized enveloping algebras called twisted Yangians, which are naturally associated with the B, C, and D series of the classical Lie algebras is studied. An explicit formula forExpand
Multiparametric and Colored Extensions of the Quantum Group GLq(N) and the Yangian Algebra Y(glN) Through a Symmetry Transformation of the Yang–Baxter Equation
Inspired by Reshetikhin's twisting procedure to obtain multiparametric extensions of a Hopf algebra, a general "symmetry transformation" of the "particle conserving" R-matrix is found such that theExpand
...
1
2
3
4
5
...