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Quantum Algebra papers — page 18

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Factorization of differential operators, quasideterminants, and nonabelian Toda field equations
We integrate nonabelian Toda field equations for root systems of types A, B, C, for functions with values in any associative algebra. The solution is expressed via quasideterminants. In the appendix…
Pavel Etingof, Israel Gelfand, Vladimir RetakhJan 9, 1997
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Heisenberg doubles and derived categories
Let A be an abelian category of finite type and homological dimension 1. Then by results of Green R(A), the extended Hall-Ringel algebra of A, has a natural Hopf algebra structure. We consider its…
M. KapranovJan 9, 1997
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Supernomial coefficients, polynomial identities and q-series
q-Analogues of the coefficients of xa in the expansion of Πj=1N (1+x+...+xj)Lj are proposed. Useful properties, such as recursion relations, symmetries and limiting theorems of…
Anne Schilling, S. Ole WarnaarJan 8, 1997
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Computer Programs for Knot Tabulation
While the problem of knot classification is far from solved, it is possible to create computer programs that can be used to tabulate knots up to a desired degree of complexity. Here we discuss the…
Charilaos AnezirisJan 8, 1997
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Quantum Schubert polynomials and quantum Schur functions
We introduce the quantum multi-Schur functions, quantum factorial Schur functions and quantum Macdonald polynomials. We prove that for restricted vexillary permutations the quantum double Schubert…
Anatol N. KirillovJan 5, 1997
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A Hopf algebra isomorphism between two realizations of the quantum affine algebra Uq(gl(2))
We consider the algebra isomorphism found by Frenkel and Ding between the RLL and the Drinfeld realizations of Uq(gl(2)). After we note that this is not a Hopf algebra isomorphism, we…
A. H. Bougourzi, A. SebbarJan 2, 1997
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Exact n-spinon dynamic structure factor of the Heisenberg model
Using the spinon picture we derive an integral representation for the exact n-spinon dynamic structure factor of the spin-1/2 Heisenberg model.
A. H. BougourziJan 2, 1997
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Quantum Double for QuasiHopf Algebras
We introduce a quantum double quasitriangular quasi-Hopf algebra D(H) associated to any quasi-Hopf algebra H. The algebra structure is a cocycle double cross product. We use categorical…
S. MajidJan 1, 1997
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Quantum Geometry and the Planck Scale
We consider some general aspects of the new noncommutative or quantum geometry coming out of the theory of quantum groups, in connection with Planck scale physics. A generalisation of Fourier or…
S. MajidJan 1, 1997
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Quantum Moduli Spaces of Flat Connections
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide…
Anton Yu. Alekseev, Volker SchomerusDec 31, 1996
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Double-loop algebras and the Fock space
The fermionic Fock space admits two different actions of the quantized enveloping algebra of > The first one is a q-deformation of the well-known level-one representation of the affine Lie…
M. Varagnolo, E. VasserotDec 30, 1996
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q-differential operator representation of the quantum superalgebra Uq(sl(M+1|N+1))
A representation of the quantum superalgebra Uq(sl(M+1|N+1)) is constructed based on the q-differential operators acting on the coherent states parameterized by coordinates. These coordinates…
Kazuhiro KimuraDec 30, 1996
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Topological Invariants For Lens Spaces And Exceptional Quantum Groups
The Reshetikhin - Turaev invariants arising from the quantum groups associated with the exceptional Lie algebras G2, F4 and E8 at odd roots of unity are constructed and explicitly computed…
R. B. ZhangDec 29, 1996
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Twisted Wess-Zumino-Witten models on elliptic curves
Investigated is a variant of the Wess-Zumino-Witten model called a twisted WZW model, which is associated to a certain Lie group bundle on a family of elliptic curves. The Lie group bundle is a…
Gen Kuroki, Takashi TakebeDec 28, 1996
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R-matrix Quantization of the Elliptic Ruijsenaars--Schneider model
It is shown that the classical L-operator algebra of the elliptic Ruijsenaars-Schneider model can be realized as a subalgebra of the algebra of functions on the cotangent bundle over the centrally…
G. E. Arutyunov, L. O. Chekhov, S. A. FrolovDec 25, 1996
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Poisson Algebra of Differential Forms
We give a natural definition of a Poisson Differential Algebra. Consistence conditions are formulated in geometrical terms. It is found that one can often locally put the Poisson structure on…
Chong-Sun Chu, Pei-Ming HoDec 24, 1996
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Differential calculi on noncommutative bundles
We introduce a category of noncommutative bundles. To establish geometry in this category we construct suitable noncommutative differential calculi on these bundles and study their basic properties.…
Markus J. Pflaum, Peter SchauenburgDec 22, 1996
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Discrete spectral triples and their symmetries
We classify 0-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure. We investigate also whether such spectral triples…
Mario Paschke, Andrzej SitarzDec 20, 1996
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Combined (q,h)-Deformation as a Nonlinear Map on Uq(sl(2))
The generators (J, J0) of the algebra Uq(sl(2)) is our starting point. An invertible nonlinear map involving, apart from q, a second arbitrary complex parameter h, defines a triplet…
B. Abdesselam, A. Chakrabarti, R. ChakrabartiDec 19, 1996
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The Lie Algebraic Structure of Differential Operators Admitting Invariant Spaces of Polynomials
We prove that the scalar and 2× 2 matrix differential operators which preserve the simplest scalar and vector-valued polynomial modules in two variables have a fundamental Lie algebraic…
Federico Finkel, Niky KamranDec 18, 1996
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Hidden symmetries and categorical representation theory
The interrelations between the inverse problems of the representation theory and the categorical representation theory are discussed.
Denis V. JurievDec 18, 1996
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Fermion Representation of Quantum Group
The spinor representation of the quantum group Uq(su(N)) is given in terms of a set of fermion creation and annihilation operators. It is shown that the q-fermion operators introduced earlier…
Minoru Hirayama, Shiori KamibayashiDec 17, 1996
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Central Extensions of the Quasi-orthogonal Lie algebras
We determine the central extensions of a whole family of Lie algebras, obtained by the method of graded contractions from so(N+1), N arbitrary. All the inhomogeneous orthogonal and pseudo-orthogonal…
J. A. de Azcarraga, F. J. Herranz, J. C. Perez Bueno et al.Dec 17, 1996
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Graded contractions and bicrossproduct structure of deformed inhomogeneous algebras
A family of deformed Hopf algebras corresponding to the classical maximal isometry algebras of zero-curvature N-dimensional spaces (the inhomogeneous algebras iso(p,q), p+q=N, as well as some of…
J. A. de Azcarraga, M. del Olmo, J. C. Perez Bueno et al.Dec 17, 1996
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Shifted Schur functions II. Binomial formula for characters of classical groups and applications
Let G be any of the complex classical groups GL(n), SO(2n+1), Sp(2n), O(2n), let g denote the Lie algebra of G, and let Z(g) denote the subalgebra of G-invariants in the universal enveloping algebra…
Andrei Okounkov, Grigori OlshanskiDec 17, 1996
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