BCJ, worldsheet quantum algebra and KZ equations

Abstract We exploit the correspondence between twisted homology and quantum group to construct an algebra explanation of the open string kinematic numerator. In this setting the representation depends on string modes, and therefore the cohomology content of the numerator, as well as the location of the punctures. We show that quantum group root system thus identified helps determine the Casimir appears in the Knizhnik-Zamolodchikov connection, which can be used to relate representations associated with different puncture locations.

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WAKIMOTO REALIZATION OF THE ELLIPTIC QUANTUM GROUP $U_{q,p}(\widehat{{\rm sl}_N})$

International Journal of Modern Physics A ◽

10.1142/s0217751x09046308 ◽

2009 ◽

Vol 24 (30) ◽

pp. 5561-5578

Author(s):

TAKEO KOJIMA

Keyword(s):

Quantum Group ◽

Free Field ◽

Quantum Algebra ◽

Free Field Realization ◽

Wakimoto Realization ◽

Arbitrary Level ◽

Elliptic Quantum

We construct a free field realization of the elliptic quantum algebra [Formula: see text] for arbitrary level k ≠ 0, -N. We study Drinfeld current and the screening current associated with [Formula: see text] for arbitrary level k. In the limit p → 0 this realization becomes q-Wakimoto realization for [Formula: see text].

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Multivariableq-Hahn polynomials as coupling coefficients for quantum algebra representations

International Journal of Mathematics and Mathematical Sciences ◽

10.1155/s0161171201012017 ◽

2001 ◽

Vol 28 (6) ◽

pp. 331-358 ◽

Cited By ~ 8

Author(s):

Hjalmar Rosengren

Keyword(s):

Tensor Product ◽

Quantum Group ◽

Quantum Algebra ◽

Coupling Coefficients ◽

Highest Weight ◽

Hahn Polynomials ◽

Highest Weight Representations

We study coupling coefficients for a multiple tensor product of highest weight representations of theSU(1,1)quantum group. These are multivariable generalizations of theq-Hahn polynomials.

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LANDAU LEVELS AND QUANTUM GROUP

Modern Physics Letters A ◽

10.1142/s0217732394000472 ◽

1994 ◽

Vol 09 (05) ◽

pp. 451-458 ◽

Cited By ~ 18

Author(s):

HARU-TADA SATO

Keyword(s):

Quantum Group ◽

Uniform Magnetic Field ◽

Periodic Potential ◽

Group Structure ◽

Quantum Algebra ◽

Wave Functions ◽

Landau Levels ◽

Group Symmetry ◽

Factor V ◽

Level Degeneracy

We find a quantum group structure in two-dimensional motions of a nonrelativistic electron in a uniform magnetic field and in a periodic potential. The representation basis of the quantum algebra is composed of wave functions of the system. The quantum group symmetry commutes with the Hamiltonian and is relevant to the Landau level degeneracy. The deformation parameter q of the quantum algebra turns out to be given by the fractional filling factor v=1/m (m odd integer).

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THE QUANTUM GROUP REALIZATIONS OF 3-D CHERN–SIMONS THEORIES

Modern Physics Letters A ◽

10.1142/s0217732395000053 ◽

1995 ◽

Vol 10 (01) ◽

pp. 39-49

Author(s):

C. RAMÍREZ ◽

L. F. URRUTIA

Keyword(s):

Quantum Group ◽

Deformation Parameter ◽

Canonical Quantization ◽

Classical Case ◽

Quantum Algebra ◽

Simons Theory ◽

R Matrix ◽

The One ◽

Chern Simons ◽

Chern Simons Theory

The algebra of the integrated connections and of their traces is considered in the one-genus sector of classical and quantum Chern–Simons theory. In the classical case this algebra is braid-like and although the corresponding Jacobi identities are satisfied, the associated r-matrix does not satisfy the classical Yang–Baxter equations. However, it turns out this algebra originates a "quantum" algebra SU (2)q given by its trace algebra. Canonical quantization of the above algebra is performed and a one-parameter expression for the operator ordering is considered. The same quantum algebra with a modified deformation parameter, nontrivially depending on ħ, is obtained.

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