Imaginary Schur-Weyl duality / Alexander Kleshchev, Robert Muth.

"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...

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Bibliographic Details
Main Authors: Kleshchëv, A. S. (Aleksandr Sergeevich) (Author), Muth, Robert, 1978- (Author)
Format: eBook
Language:English
Published: Providence, Rhode Island : American Mathematical Society, 2017.
Series:Memoirs of the American Mathematical Society ; no. 1157.
Subjects:
Online Access:Click for online access

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100 1 |a Kleshchëv, A. S.  |q (Aleksandr Sergeevich),  |e author.  |1 https://id.oclc.org/worldcat/entity/E39PCjHYcF6vgmxVjYYtJbk343 
245 1 0 |a Imaginary Schur-Weyl duality /  |c Alexander Kleshchev, Robert Muth. 
264 1 |a Providence, Rhode Island :  |b American Mathematical Society,  |c 2017. 
264 4 |c ©2016 
300 |a 1 online resource (xvii, 83 pages) :  |b illustrations 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
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490 1 |a Memoirs of the American Mathematical Society,  |x 0065-9266 ;  |v volume 245, number 1157 
588 0 |a Online resource; title from PDF title page (viewed November 18, 2016). 
500 |a "Volume 245, Number 1157 (second of 6 numbers), January 2017." 
504 |a Includes bibliographical references (pages 81-83). 
505 0 0 |t Chapter 1. Introduction  |t Chapter 2. Preliminaries  |t Chapter 3. Khovanov-Lauda-Rouquier algebras  |t Chapter 4. Imaginary Schur-Weyl duality  |t Chapter 5. Imaginary Howe duality  |t Chapter 6. Morita equaivalence  |t Chapter 7. On formal characters of imaginary modules  |t Chapter 8. Imaginary tensor space for non-simply-laced types. 
520 3 |a "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 
650 0 |a Duality theory (Mathematics) 
650 0 |a Representations of Lie algebras. 
650 0 |a Lie algebras. 
650 7 |a Duality theory (Mathematics)  |2 fast 
650 7 |a Lie algebras  |2 fast 
650 7 |a Representations of Lie algebras  |2 fast 
700 1 |a Muth, Robert,  |d 1978-  |e author.  |1 https://id.oclc.org/worldcat/entity/E39PCjH6KJxyMkwvmKWFdGWKJP 
710 2 |a American Mathematical Society,  |e publisher. 
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776 0 8 |i Print version:  |a Kleshchëv, A.S.  |t Imaginary Schur-Weyl duality /  |x 0065-9266  |z 9781470422493  |w (DLC) 2016053200 
830 0 |a Memoirs of the American Mathematical Society ;  |v no. 1157. 
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