Skip to content

Quantum Algebra papers — page 10

q-algBrowse archive

Deforming the Lie algebra of vector fields on S1 inside the Poisson algebra on T*S1
We study deformations of the standard embedding of the Lie algebra (S1) of smooth vector fields on the circle, into the Lie algebra of functions on the cotangent bundle T*S1 (with respect…
V. Ovsienko, C. RogerJul 7, 1997
Learn
Drinfeld twist for quantum su(2) in the adjoint representation
We give a detailed description of the adjoint representation of Drinfeld's twist element, as well as of its coproduct, for suq(2). We also discuss, as applications, the computation of the…
Chryssomalis ChryssomalakosJul 4, 1997
Learn
On BC type basic hypergeometric orthogonal polynomials
The five parameter family of multivariable Askey-Wilson polynomials is studied with four parameters generically complex. The multivariable Askey-Wilson polynomials form an orthogonal system with…
Jasper V. StokmanJul 3, 1997
Learn
Characters of Demazure modules and solvable lattice models
We study the path realization of Demazure crystals related to solvable lattice models in statistical mechanics. Various characters are represented in a unified way as the sums over one dimensional…
A. Kuniba, K. C. Misra, M. Okado et al.Jul 3, 1997
Learn
A note on quivers with symmetries
We show that the bases of irreducible integrable highest weight module of a non-symmetric Kac-Moody algebra, which is associated to a quiver with a nontrivial admissible automorphism, can be…
Feng XuJul 2, 1997
Learn
Reflections on Topological Quantum Field Theory
(Talk presented at the XVth Workshop on Geometric Methods in Physics, Quantizations, Deformations and Coherent States, in Bialowieza, Poland, July 1-7, 1996.) The aim of this article is to introduce…
Roger PickenJul 1, 1997
Learn
Symmetric Jack polynomials from non-symmetric theory
The theory of non-symmetric Jack polynomials is developed independently of the theory of symmetric Jack polynomials, and this theory together with the relationship between the non-symmetric,…
T. H. Baker, P. J. ForresterJul 1, 1997
Learn
General Construction of Nonstandard Rh-matrices as Contraction Limits of Rq-matrices
A class of transformations of Rq-matrices is introduced such that the q 1 limit gives explicit nonstandard Rh-matrices. The transformation matrix is singular itself at q 1 limit.…
B. Abdesselam, A. Chakrabarti, R. ChakrabartiJun 28, 1997
Learn
Reflection Equation Algebra of a (h,w)-deformed Oscillator
We consider the reflection equation algebra for a finite dimensional R-matrix for the (h,w)-deformed Heisenberg algebra Uh,w(h(4)). A representation of the reflection matrix K is…
Boucif Abdesselam, Ranabir ChakrabartiJun 27, 1997
Learn
Particles in Singular Magnetic Field
An algebraic formalism for description of quantum states of charged particle with spin moving in two-dimensional space under influence of singular magnetic field is developed in terms of graded…
Wladyslaw MarcinekJun 24, 1997
Learn
Conformal Modules
In this paper we study a class of modules over infinite-dimensional Lie (super)algebras, which we call conformal modules. In particular we classify and construct explicitly all irreducible conformal…
Shun-Jen Cheng, Victor KacJun 23, 1997
Learn
The structure of quantum Lie algebras for the classical series Bl, Cl and Dl
The structure constants of quantum Lie algebras depend on a quantum deformation parameter q and they reduce to the classical structure constants of a Lie algebra at q=1. We explain the relationship…
Gustav W. Delius, Christopher Gardner, Mark D. GouldJun 22, 1997
Learn
Intertwining operator algebras and vertex tensor categories for affine Lie algebras
We apply the general theory of tensor products of modules for a vertex operator algebra developed in our papers hep-th/9309076, hep-th/9309159, hep-th/9401119, q-alg/9505018, q-alg/9505019 and…
Yi-Zhi Huang, James LepowskyJun 22, 1997
Learn
Singular deformations of Lie algebras on an example
The notion of singular one-parameter deformation of a Lie algebra is introduced. It is shown that the complex infinite-dimensional Lie algebra of polynomial vector fields in C with trivial 1-jet at…
Alice Fialowski, Dmitry FuchsJun 20, 1997
Learn
Quantum geometry of field extensions
We show that noncommutative differential forms on k[x], k a field, are of the form Ω1=kλ[x] where kλ⊃ k is a field extension. We compute the case C⊃ R explicitly, where Ω1…
S. MajidJun 19, 1997
Learn
Crystal Bases and Young Tableaux
Let B be the crystal basis of the minus part of the quantized enveloping algebra of a semi-simple Lie algebra. Kashiwara has shown that B has a combinatorial description in terms of an embedding of B…
Gerald CliffJun 19, 1997
Learn
Classical dynamical r-matrices for Calogero-Moser systems and their generalizations
We present a derivation of the dynamical r-matrices of the Calogero-Moser models using the Hamiltonian reduction procedure to get general formulae. We describe the dynamical r-matrices thus found for…
J. AvanJun 19, 1997
Learn
Towards Deformed Chiral Algebras
We describe a new algebraic structure of "deformed chiral algebra" motivated by the study of the deformed W-algebras. We use it to gain some insights into the deformed Virasoro algebra.
Edward Frenkel, Nikolai ReshetikhinJun 18, 1997
Learn
The number of primitive Vassiliev invariants up to degree 12
We present algorithms giving upper and lower bounds for the number of independent primitive rational Vassiliev invariants of degree m modulo those of degree m-1. The values have been calculated for…
Jan A. KneisslerJun 18, 1997
Learn
A PBW basis for Lusztig's form of untwisted affine quantum groups
Let g be an untwisted affine Kac-Moody algebra over the field K \, , and let Uq(g) be the associated quantum enveloping algebra; let Uq(g) be the…
Fabio GavariniJun 17, 1997
Learn
On classification of dynamical r-matrices
Using recent results of P. Etingof and A. Varchenko on the Classical Dynamical Yang-Baxter equation, we reduce the classification of dynamical r-matrices r on a commutative subalgebra l of a Lie…
Olivier SchiffmannJun 17, 1997
Learn
Quantum differentials and the q-monopole revisited
The q-monopole bundle introduced previously is extended to a general construction for quantum group bundles with non-universal differential calculi. We show that the theory applies to several other…
Tomasz Brzezinski, Shahn MajidJun 17, 1997
Learn
The space of free coherent states is isomorphic to the space of distributions on p-adic numbers
Free coherent states for a system with p degrees of freedom are defined. An isomorphism of the space of free coherent states to the space of distributions on p-adic disk is constructed.
Sergei KozyrevJun 17, 1997
Learn
Intertwining Operators for a Degenerate Double Affine Hecke Algebra and Multivariable Orthogonal Polynomials
Operators that intertwine representations of a degenerate version of the double affine Hecke algebra are introduced. Each of the representations is related to multi-variable orthogonal polynomials…
Saburo KakeiJun 17, 1997
Learn
A Poincaré-Birkhoff-Witt theorem for generalized color Lie algebras
A proof of Poincaré-Birkhoff-Witt theorem is given for a class of generalized Lie algebras closely related to the Gurevich S-Lie algebras. As concrete examples, we construct the positive (negative)…
Cesar BautistaJun 15, 1997
Learn
← PreviousPage 10Next →