Imaginary SchurWeyl duality / Alexander Kleshchev and Robert Muth.
By: Kleshchev, Aleksandr [author].
Contributor(s): Muth, Robert [author].
Material type: TextSeries: Memoirs of the American Mathematical Society, v 245, no 1157.Publisher: Providence : American Mathematical Society, 2017Description: xvii, 83 pages : illustrations ; 26 cm.ISBN: 9781470422493 (alk. paper).Subject(s): Duality theory (Mathematics)  Representations of Lie algebras  Lie algebrasDDC classification: 510Item type  Current location  Call number  Status  Date due  Barcode  Item holds  

Books 
ISI Library, Kolkata

510 Am512 (Browse shelf)  Available  138199 
"Volume 245, number 1157 (second of 6 numbers), January 2017."
Includes bibliographical references.
1. Introduction 
2. Preliminaries 
3. KhovanovLaudaRouquier alebras 
4. Imaginary SchurWeyl duality 
5. Imaginary Howe duality 
6. Morita equaivalence 
7. On formal characters of imaginary modules 
8. Imaginary tensor space for nonsimplylaced types.
The authors study imaginary representations of the KhovanovLaudaRouquier 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 modulesone for each real positive root for the corresponding affine root system ${\tt X}_l^{(1)}$, as well as irreducible imaginary modulesone for each $l$multiplication. The authors study imaginary modules by means of ``imaginary SchurWeyl 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 GelfandGraev representations, Ringel duality and the JacobiTrudy formula.
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