Polynomial relations in the centre of U$_{q}$(sl(N))

When the parameter of deformation q is a m-th root of unity, the centre of U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new generators, which are basically the m-th powers of all the Cartan generators of U_q(sl(N)). All these central elements are however not independent. In...

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Detalles Bibliográficos
Autores principales: Arnaudon, Daniel, Bauer, Michel
Lenguaje:eng
Publicado: 1994
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1007/BF00805857
http://cds.cern.ch/record/254220
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author Arnaudon, Daniel
Bauer, Michel
author_facet Arnaudon, Daniel
Bauer, Michel
author_sort Arnaudon, Daniel
collection CERN
description When the parameter of deformation q is a m-th root of unity, the centre of U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new generators, which are basically the m-th powers of all the Cartan generators of U_q(sl(N)). All these central elements are however not independent. In this letter, generalising the well-known case of U_q(sl(2)), we explicitly write polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.
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institution Organización Europea para la Investigación Nuclear
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publishDate 1994
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spelling cern-2542202020-07-23T02:48:05Zdoi:10.1007/BF00805857http://cds.cern.ch/record/254220engArnaudon, DanielBauer, MichelPolynomial relations in the centre of U$_{q}$(sl(N))Mathematical Physics and MathematicsWhen the parameter of deformation q is a m-th root of unity, the centre of U_q(sl(N))$ contains, besides the usual q-deformed Casimirs, a set of new generators, which are basically the m-th powers of all the Cartan generators of U_q(sl(N)). All these central elements are however not independent. In this letter, generalising the well-known case of U_q(sl(2)), we explicitly write polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.When the parameter of deformation $q$ is a root of unity, the centre of ${\cal U}_q(sl(N))$ contains, besides the usual $q$-deformed Casimirs, a set of new generators which are basically the $m$-th powers of all the Cartan generators of ${\cal U}_q(sl(N))$. All these central elements are however not independent. In this letter, generalising the well-known case of ${\cal U}_q(sl(2))$, we write explicitely polynomial relations satisfied by the generators of the centre. Application to the parametrization of irreducible representations and to fusion rules are sketched.hep-th/9310030CERN-TH-7025-93ENSLAPP-A-437-93CERN-TH-7025-93ENSLAPP-A-437oai:cds.cern.ch:2542201994
spellingShingle Mathematical Physics and Mathematics
Arnaudon, Daniel
Bauer, Michel
Polynomial relations in the centre of U$_{q}$(sl(N))
title Polynomial relations in the centre of U$_{q}$(sl(N))
title_full Polynomial relations in the centre of U$_{q}$(sl(N))
title_fullStr Polynomial relations in the centre of U$_{q}$(sl(N))
title_full_unstemmed Polynomial relations in the centre of U$_{q}$(sl(N))
title_short Polynomial relations in the centre of U$_{q}$(sl(N))
title_sort polynomial relations in the centre of u$_{q}$(sl(n))
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1007/BF00805857
http://cds.cern.ch/record/254220
work_keys_str_mv AT arnaudondaniel polynomialrelationsinthecentreofuqsln
AT bauermichel polynomialrelationsinthecentreofuqsln

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