Imaginary Schur-Weyl duality
by Kleshchëv, A. S., (Aleksandr Sergeevich)
"We 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 X<sub>l</sub><sup>(1)</sup>, as well as irreducible imaginary modules--one for each l-mu…
Read More ↓Title Statements
- Full title :Imaginary Schur-Weyl duality / Alexander Kleshchev, Robert Muth.
Summary
"We 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 X<sub>l</sub><sup>(1)</sup>, as well as irreducible imaginary modules--one for each l-multiplication. We study imaginary modules by means of 'imaginary Schur-Weyl duality'. We introduce an imaginary analogue of tensor space and the imaginary Schur algebra. We construct a projective generator for the imaginary Schur algebra, which yields a Morita equivalence between the imaginary and the classical Schur algebra. We construct imaginary analogues of Gelfand-Graev representations, Ringel duality and the Jacobi-Trudy formula."--Page v
Read More ↓Edition Statements
- Publication Date:©2016
Publication Statements
- Publisher(s):American mathematical Society
- Place of Publication:Providence, Rhode Island
- Language:eng
- Publication Date:©2016
Notes
"Volume 245, Number 1157 (second of 6 numbers), January 2017."
The Physical Object
- Description:1 online resource (xvii, 83 pages) : : illustrations
Edition Identifiers
- ISBN:9781470436032, 1470436035, 1470422492, 9781470422493
- oclc:ocn965547796
- LC Classification:QA564
- Dewey Decimal:512/.482
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