Cargando…

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...

Descripción completa

Detalles Bibliográficos
Autores principales: Kleshchev, Alexander, Muth, Robert
Lenguaje:eng
Publicado: American Mathematical Society 2017
Materias:
Acceso en línea:http://cds.cern.ch/record/2279718
_version_ 1780955464584921088
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