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Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1
A simple connection between the universal R matrix of U_q(sl(2)) (for spins \demi and J) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant...
Autores principales: | , , |
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Lenguaje: | eng |
Publicado: |
1995
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.1007/BF02104913 http://cds.cern.ch/record/279303 |
_version_ | 1780887808810942464 |
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author | Cremmer, Eugene Gervais, Jean-Loup Schnittger, Jens |
author_facet | Cremmer, Eugene Gervais, Jean-Loup Schnittger, Jens |
author_sort | Cremmer, Eugene |
collection | CERN |
description | A simple connection between the universal R matrix of U_q(sl(2)) (for spins \demi and J) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant operators. It allows us to derive the quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of U_q(sl(2)) realized by (what we call) fixed point commutation relations. This is explained by showing that the link between the algebra of field transformations and that of the co-product generators is much weaker than previously thought. The central charges of our extended U_q(sl(2)) algebra, which includes the Liouville zero-mode momentum in a nontrivial way are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quantum-group symmetry U_q(sl(2))\odot U_{\qhat}(sl(2)) related to the presence of both of the screening charges of 2D gravity. |
id | cern-279303 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 1995 |
record_format | invenio |
spelling | cern-2793032023-03-14T18:55:47Zdoi:10.1007/BF02104913http://cds.cern.ch/record/279303engCremmer, EugeneGervais, Jean-LoupSchnittger, JensOperator coproduct-realization of quantum group transformations in two dimensional gravity, 1Particle Physics - TheoryA simple connection between the universal R matrix of U_q(sl(2)) (for spins \demi and J) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant operators. It allows us to derive the quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of U_q(sl(2)) realized by (what we call) fixed point commutation relations. This is explained by showing that the link between the algebra of field transformations and that of the co-product generators is much weaker than previously thought. The central charges of our extended U_q(sl(2)) algebra, which includes the Liouville zero-mode momentum in a nontrivial way are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quantum-group symmetry U_q(sl(2))\odot U_{\qhat}(sl(2)) related to the presence of both of the screening charges of 2D gravity.A simple connection between the universal $R$ matrix of $U_q(sl(2))$ (for spins $\demi$ and $J$) and the required form of the co-product action of the Hilbert space generators of the quantum group symmetry is put forward. This gives an explicit operator realization of the co-product action on the covariant operators. It allows us to derive the quantum group covariance of the fusion and braiding matrices, although it is of a new type: the generators depend upon worldsheet variables, and obey a new central extension of $U_q(sl(2))$ realized by (what we call) fixed point commutation relations. This is explained by showing that the link between the algebra of field transformations and that of the co-product generators is much weaker than previously thought. The central charges of our extended $U_q(sl(2))$ algebra, which includes the Liouville zero-mode momentum in a nontrivial way are related to Virasoro-descendants of unity. We also show how our approach can be used to derive the Hopf algebra structure of the extended quantum-group symmetry $U_q(sl(2))\odot U_{\qhat}(sl(2))$ related to the presence of both of the screening charges of 2D gravity.hep-th/9503198CERN-TH-95-48CERN-TH-95-048LPTENS-95-11CERN-TH-95-48LPT-ENS-95-11oai:cds.cern.ch:2793031995-03-28 |
spellingShingle | Particle Physics - Theory Cremmer, Eugene Gervais, Jean-Loup Schnittger, Jens Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1 |
title | Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1 |
title_full | Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1 |
title_fullStr | Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1 |
title_full_unstemmed | Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1 |
title_short | Operator coproduct-realization of quantum group transformations in two dimensional gravity, 1 |
title_sort | operator coproduct-realization of quantum group transformations in two dimensional gravity, 1 |
topic | Particle Physics - Theory |
url | https://dx.doi.org/10.1007/BF02104913 http://cds.cern.ch/record/279303 |
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