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Imaginary Schur-Weyl duality
The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal sys...
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Lenguaje: | eng |
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American Mathematical Society
2017
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Acceso en línea: | http://cds.cern.ch/record/2279718 |
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author | Kleshchev, Alexander Muth, Robert |
author_facet | Kleshchev, Alexander Muth, Robert |
author_sort | Kleshchev, Alexander |
collection | CERN |
description | The authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules-one for each real positive root for the corresponding affine root system {\tt X}_l^{(1)}, as well as irreducible imaginary modules-one for each l-multiplication. The authors study imaginary modules by means of "imaginary Schur-Weyl duality" and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula. |
id | cern-2279718 |
institution | Organización Europea para la Investigación Nuclear |
language | eng |
publishDate | 2017 |
publisher | American Mathematical Society |
record_format | invenio |
spelling | cern-22797182021-04-21T19:05:51Zhttp://cds.cern.ch/record/2279718engKleshchev, AlexanderMuth, RobertImaginary Schur-Weyl dualityMathematical Physics and MathematicsThe authors study imaginary representations of the Khovanov-Lauda-Rouquier algebras of affine Lie type. Irreducible modules for such algebras arise as simple heads of standard modules. In order to define standard modules one needs to have a cuspidal system for a fixed convex preorder. A cuspidal system consists of irreducible cuspidal modules-one for each real positive root for the corresponding affine root system {\tt X}_l^{(1)}, as well as irreducible imaginary modules-one for each l-multiplication. The authors study imaginary modules by means of "imaginary Schur-Weyl duality" and introduce an imaginary analogue of tensor space and the imaginary Schur algebra. They construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra, and construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula.American Mathematical Societyoai:cds.cern.ch:22797182017 |
spellingShingle | Mathematical Physics and Mathematics Kleshchev, Alexander Muth, Robert Imaginary Schur-Weyl duality |
title | Imaginary Schur-Weyl duality |
title_full | Imaginary Schur-Weyl duality |
title_fullStr | Imaginary Schur-Weyl duality |
title_full_unstemmed | Imaginary Schur-Weyl duality |
title_short | Imaginary Schur-Weyl duality |
title_sort | imaginary schur-weyl duality |
topic | Mathematical Physics and Mathematics |
url | http://cds.cern.ch/record/2279718 |
work_keys_str_mv | AT kleshchevalexander imaginaryschurweylduality AT muthrobert imaginaryschurweylduality |