| Description |
1 online resource (xvii, 83 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; volume 245, number 1157 |
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Memoirs of the American Mathematical Society ; no. 1157.
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| Contents |
Chapter 1. Introduction Chapter 2. Preliminaries Chapter 3. Khovanov-Lauda-Rouquier algebras Chapter 4. Imaginary Schur-Weyl duality Chapter 5. Imaginary Howe duality Chapter 6. Morita equaivalence Chapter 7. On formal characters of imaginary modules Chapter 8. Imaginary tensor space for non-simply-laced types |
| 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 |
| Notes |
"Volume 245, Number 1157 (second of 6 numbers), January 2017." |
| Bibliography |
Includes bibliographical references (pages 81-83) |
| Notes |
Online resource; title from PDF title page (viewed November 18, 2016) |
| Subject |
Duality theory (Mathematics)
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Representations of Lie algebras.
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Lie algebras.
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Duality theory (Mathematics)
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Lie algebras
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Representations of Lie algebras
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| Form |
Electronic book
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| Author |
Muth, Robert, 1978- author.
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American Mathematical Society, publisher
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| ISBN |
9781470436032 |
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1470436035 |
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1470422492 |
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9781470422493 |
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