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Quantum Algebra papers — page 45

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Traces of intertwining operators and Macdonald's polynomials
Let Φ:V V U be an intertwining operator between representations of a simple Lie algebra (quantum group, affine Lie algebra). We define its generalized character to be the following…
Alexander KirillovMar 21, 1995
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On some nonlinear extensions of the angular momentum algebra
Deformations of the Lie algebras so(4), so(3,1), and e(3) that leave their so(3) subalgebra undeformed and preserve their coset structure are considered. It is shown that such deformed algebras are…
C. QuesneMar 17, 1995
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q-Deformation of the Lorentz Group
We describe a q-deformation of the Lorentz group in terms of a q-deformation of the van der Waerden spinor algebra.
Robert J. FinkelsteinMar 16, 1995
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Field Theory on q=-1 Quantum Plane
We build the q=-1 defomation of plane on a product of two copies of algebras of functions on the plane. This algebra constains a subalgebra of functions on the plane. We present general scheme…
Andrzej SitarzMar 16, 1995
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Macdonald's Evaluation Conjectures, Difference Fourier Transform, and Applications
This paper contains the proof of Macdonald's duality and evaluation conjectures, the definition of the difference Fourier transform, the recurrence theorem generalizing Pieri rules, and the…
Ivan CherednikMar 14, 1995
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Heisenberg Double and Pentagon Relation
It is shown that the Heisenberg double has a canonical element, satisfying the pentagon relation. From a given invertible constant solution to the pentagon relation one can restore the structure of…
R. M. KashaevMar 14, 1995
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Phase Space Reduction for Star-Products: An Explicit Construction for CPn
We derive a closed formula for a star-product on complex projective space and on the domain SU(n+1)/S(U(1)× U(n)) using a completely elementary construction: Starting from the standard…
M. Bordemann, M. Brischle, C. Emmrich et al.Mar 9, 1995
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Lie Algebroids Associated to Poisson Actions
This work is motivated by a result of Drinfeld on Poisson homogeneous spaces. For each Poisson manifold P with a Poisson action by a Poisson Lie group G, we describe a Lie algebroid structure on…
Jiang-Hua LuMar 8, 1995
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Higher-dimensional Algebra and Topological Quantum Field Theory
The study of topological quantum field theories increasingly relies upon concepts from higher-dimensional algebra such as n-categories and n-vector spaces. We review progress towards a definition of…
John C. Baez, James DolanMar 5, 1995
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Crystal Graphs and q-Analogues of Weight Multiplicities for the Root System An
We give an expression of the q-analogues of the multiplicities of weights in irreducible n+1-modules in terms of the geometry of the crystal graph attached to the corresponding…
A. Lascoux, B. Leclerc, J. -Y. ThibonMar 4, 1995
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A New Null-Plane Quantum Poincare Algebra
A new quantum deformation, which we call null-plane, of the (3+1) Poincaré algebra is obtained. The algebraic properties of the classical null-plane description are generalized to this quantum…
A. Ballesteros, F. J. Herranz, M. A. del Olmo et al.Feb 28, 1995
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The character table of the Hecke algebra Hn(q) in terms of traces of products of Murphy operators
The traces of the Murphy operators of the Hecke algebra Hn(q), and of products of sets of Murphy operators with non-consecutive indices, can be evaluated by a straightforward recursive procedure.…
J. Katriel, B. Abdesselam, A. ChakrabartiFeb 27, 1995
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Groups of ribbon knots
Given a positive integer n, we say that two knots are Vn-equivalent if they have the same Vassiliev invariants of order n. We showed that the Vn-equivalence classes of ribbon knots form…
Ka Yi NgFeb 24, 1995
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Hecke algebras, Uqsln, and the Donald--Flanigan conjecture for Sn
To each partition p of n we associate in a canonical way a simple Sn module with an orthogonal basis indexed by Young diagrams in a way which carries over immediately to the quantized…
Murray Gerstenhaber, Mary E. SchapsFeb 23, 1995
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Some Rational Vertex Algebras
Let L((n- 3 2)Λ0), n ∈ N, be a vertex operator algebra associated to the irreducible highest weight module L((n- 3 2)Λ0) for a symplectic affine Lie algebra. We find a…
Drazen AdamovicFeb 22, 1995
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Some remarks on the q-Poincare algebra in R-matrix form
The braided approach to q-deformation (due to the author and collaborators) gives natural algebras R21u1Ru2=u2R21u1R and R21x1x2=x2x1R for q-Minkowski and q-Euclidean spaces…
S. MajidFeb 20, 1995
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Characteristic Relations for Quantum Matrices
General algebraic properties of the algebras of vector fields over quantum linear groups GLq(N) and SLq(N) are studied. These quantum algebras appears to be quite similar to the classical…
P. Pyatov, P. SaponovFeb 20, 1995
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Langlands Reciprocity for Algebraic Surfaces
This note is an attempt to extend "Geometric Langlands Conjecture" from algebraic curves to algebraic surfaces. We introduce certain Hecke-type operators on vector bundles on an algebraic…
Victor Ginzburg, Mikhail Kapranov, Eric VasserotFeb 20, 1995
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Weight Vectors of the Basic A1(1)-Module and the Littlewood-Richardson Rule
The basic representation of is studied. The weight vectors are represented in terms of Schur functions. A suitable base of any weight space is given. Littlewood-Richardson rule appears in the…
Susumu Ariki, Tatsuhiro Nakajima, Hiro-Fumi YamadaFeb 18, 1995
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On the relation between two quantum group invariants of 3-cobordisms
We prove in the context of quantum groups at even roots of unity that a Turaev-Viro type invariant of a 3-dimensional cobordism M equals the tensor product of the Reshetikhin-Turaev invariants of M…
Anna Beliakova, Bergfinnur DurhuusFeb 16, 1995
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Representations of Yangians with Gelfand-Zetlin Bases
We study certain family of finite-dimensional modules over the Yangian Y(glN). The algebra Y(glN) comes equipped with a distinguished maximal commutative subalgebra A(gln) generated by the…
Maxim Nazarov, Vitaly TarasovFeb 13, 1995
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Quantum Cohomology of a Product
The operation of tensor product of Cohomological Field Theories (or algebras over genus zero moduli operad) introduced in an earlier paper by the authors is described in full detail, and the proof of…
M. Kontsevich, Yu. Manin, R. KaufmannFeb 13, 1995
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Dynamical Symmetries in q-deformed Quantum Mechanics
The dynamical algebra of the q-deformed harmonic oscillator is constructed. As a result, we find the free deformed Hamiltonian as well as the Hamiltonian of the deformed oscillator as a complicated,…
A. Lorek, J. WessFeb 8, 1995
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Cohomology and Deformation of Leibniz Pairs
Cohomology and deformation theories are developed for Poisson algebras starting with the more general concept of a Leibniz pair, namely of an associative algebra A together with a Lie algebra L…
M. Flato, M. Gerstenhaber, A. A. VoronovFeb 6, 1995
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Realization of Vector fields for Quantum Groups as Pseudodifferential Operators on Quantum Spaces
The vector fields of the quantum Lie algebra are described for the quantum groups GLq(N), SLq(N) and SOq(N) as pseudodifferential operators on the linear quantum spaces covariant under the…
Chong-Sun Chu, Bruno ZuminoFeb 3, 1995
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