Skip to content

Quantum Algebra papers — page 28

q-algBrowse archive

Bosonization of Admissible Representations of Uq(sl2) at Level -12 and q-Vertex Operators
We construct a representation of Uq(sl2) at level -1/2 by using the bosonic Fock spaces. The irreducible modules are obtained as the kernel of a certain operator, in contrast to the…
Yoshitaka KoyamaMay 20, 1996
Learn
Quantum Lie algebras; their existence, uniqueness and q-antisymmetry
Quantum Lie algebras are generalizations of Lie algebras which have the quantum parameter h built into their structure. They have been defined concretely as certain submodules of the quantized…
Gustav W. Delius, Mark D. GouldMay 17, 1996
Learn
Melvin-Morton conjecture and primitive Feynman diagrams
We give a very short proof of the Melvin-Morton conjecture relating the colored Jones polynomial and the Alexander polynomial of knots. The proof is based on the explicit evaluation of the…
Arkady VaintrobMay 17, 1996
Learn
A new class of deformed special functions from quantum homogeneous spaces
We study the most elementary aspects of harmonic analysis on a homogeneous space of a deformation of the two-dimensional Euclidean group, admitting generalizations to dimensions three and four, whose…
F. Bonechi, R. Giachetti, M. A. del Olmo et al.May 17, 1996
Learn
Introduction to Quantum Lie Algebras
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras . The quantum Lie bracket…
Gustav W. DeliusMay 17, 1996
Learn
Burau representation and random walk on string links
Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string…
Xiao-Song Lin, Feng Tian, Zhenghan WangMay 15, 1996
Learn
Algebraic Bethe ansatz for the elliptic quantum group Eτ,η(sl2)
To each representation of the elliptic quantum group Eτ,η(sl2) is associated a family of commuting transfer matrices. We give common eigenvectors by a version of the algebraic Bethe ansatz…
Giovanni Felder, Alexander VarchenkoMay 15, 1996
Learn
Deformed boson algebras and the quantum double construction
The quantum double construction of a q-deformed boson algebra possessing a Hopf algebra structure is carried out explicitly. The R-matrix thus obtained is compared with the existing literature.
D. S. McAnally, I. TsohantjisMay 15, 1996
Learn
On Casimir's Ghost
We define on the universal enveloping superalgebra of osp(1|2n) a nonstandard adjoint action, endowing it with a module structure. This allows, in particular, to construct a bosonic operator which…
D. Arnaudon, M. Bauer, L. FrappatMay 14, 1996
Learn
Scasimir operator, Scentre and Representations of Uq(osp(1|2))
A bosonic operator of Uq(osp(1|2)) that anticommutes with the fermionic generators appears to be useful to describe the relations in the centre of Uq(osp(1|2)) for q a root of unity (in the…
D. Arnaudon, M. BauerMay 14, 1996
Learn
Vassiliev Invariants and Gleam Polynomials
It was shown by Goussarov that Vassiliev invariants are polynomials in the gleams for a fixed Turaev shadow. In this paper we show that Vassiliev invariants are almost characterized by this fact. We…
Urs BurriMay 14, 1996
Learn
On the uniqueness of the Moyal structure of phase-space functions
It is shown that the only associative algebras with a trivial center defined on functions of N by an integral kernel are generalized Moyal algebras, corresponding to some particular operator…
C. Tzanakis, A. DimakisMay 13, 1996
Learn
A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials
We define a one-parameter family of two-sided coideals in Uq(gl(n)) and study the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group Uq(n). The…
M. S. Dijkhuizen, M. NoumiMay 13, 1996
Learn
Group-like elements in quantum groups, and Feigin's conjecture
Let A be an arbitrary symmetrizable Cartan matrix of rank r, and n= n+ be the standard maximal nilpotent subalgebra in the Kac-Moody algebra associated with A (thus, n is…
Arkady BerensteinMay 12, 1996
Learn
Centre and Representations of Uq(sl(2|1)) at Roots of Unity
Quantum groups at roots of unity have the property that their centre is enlarged. Polynomial equations relate the standard deformed Casimir operators and the new central elements. These relations are…
B. Abdesselam, D. Arnaudon, M. BauerMay 10, 1996
Learn
(Shifted) Macdonald Polynomials: q-Integral Representation and Combinatorial Formula
We extend some results about shifted Schur functions to the general context of shifted Macdonald polynomials. We obtain two explicit formulas for these polynomials: a q-integral representation and…
Andrei OkounkovMay 9, 1996
Learn
Intertwining Operators of Double Affine Hecke Algebras
A systematic study of the representation theory of double affine Hecke algebras and related harmonic analysis is started in this paper. Continuing the previous papers we use the technique of…
Ivan CherednikMay 9, 1996
Learn
A Fedosov Star Product of Wick Type for Kähler Manifolds
In this letter we compute some elementary properties of the Fedosov star product of Weyl type, such as symmetry and order of differentiation. Moreover, we define the notion of a star product of Wick…
M. Bordemann, S. WaldmannMay 8, 1996
Learn
General methods for constructing bispectral operators
We present methods for obtaining new solutions to the bispectral problem. We achieve this by giving its abstract algebraic version suitable for generalizations. All methods are illustrated by new…
B. Bakalov, E. Horozov, M. YakimovMay 8, 1996
Learn
Quantum Gauge Transformations and Braided Structure on Quantum Principal Bundles
It is shown that every quantum principal bundle is braided, in the sense that there exists an intrinsic braid operator twisting the functions on the bundle. A detailed algebraic analysis of this…
Mico DurdevicMay 5, 1996
Learn
Quantum Classifying Spaces and Universal Quantum Characteristic Classes
A construction of the noncommutative-geometric counterparts of classical classifying spaces is presented, for general compact matrix quantum structure groups. A quantum analogue of the classical…
Mico DurdevicMay 5, 1996
Learn
Quantum Principal Bundles and Their Characteristic Classes
A brief exposition of the general theory of characteristic classes of quantum principal bundles is given. The theory of quantum characteristic classes incorporates ideas of classical Weil theory into…
Mico DurdevicMay 5, 1996
Learn
General Frame Structures On Quantum Principal Bundles
A noncommutative-geometric generalization of the classical formalism of frame bundles is developed, incorporating into the theory of quantum principal bundles the concept of the Levi-Civita…
Mico DurdevicMay 5, 1996
Learn
First-Order Differential Calculi Over Multi-Braided Quantum Groups
A differential calculus of the first order over multi-braided quantum groups is developed. In analogy with the standard theory, left/right-covariant and bicovariant differential structures are…
Mico DurdevicMay 5, 1996
Learn
q-Difference raising operators for Macdonald polynomials and the integrality of transition coefficients
We study certain q-difference raising operators for Macdonald polynomials (of type An-1) which are originated from the q-difference-reflection operators introduced in our previous paper.…
Anatol N. Kirillov, Masatoshi NoumiMay 4, 1996
Learn
← PreviousPage 28Next →