Imaginary Schur-Weyl Duality. (Record no. 128017)
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| fixed length control field | 04992nam a22004813i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC4908273 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240729131328.0 |
| 006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS | |
| fixed length control field | m o d | |
| 007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION | |
| fixed length control field | cr cnu|||||||| |
| 008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION | |
| fixed length control field | 240724s2017 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470436032 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470422493 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC4908273 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL4908273 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (CaPaEBR)ebr11409819 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)965547796 |
| 040 ## - CATALOGING SOURCE | |
| Original cataloging agency | MiAaPQ |
| Language of cataloging | eng |
| Description conventions | rda |
| -- | pn |
| Transcribing agency | MiAaPQ |
| Modifying agency | MiAaPQ |
| 050 #4 - LIBRARY OF CONGRESS CALL NUMBER | |
| Classification number | QA564.K547 2017 |
| 082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER | |
| Classification number | 512.48199999999997 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Kleshchev, Alexander. |
| 245 10 - TITLE STATEMENT | |
| Title | Imaginary Schur-Weyl Duality. |
| 250 ## - EDITION STATEMENT | |
| Edition statement | 1st ed. |
| 264 #1 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Place of production, publication, distribution, manufacture | Providence : |
| Name of producer, publisher, distributor, manufacturer | American Mathematical Society, |
| Date of production, publication, distribution, manufacture, or copyright notice | 2017. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2016. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (108 pages) |
| 336 ## - CONTENT TYPE | |
| Content type term | text |
| Content type code | txt |
| Source | rdacontent |
| 337 ## - MEDIA TYPE | |
| Media type term | computer |
| Media type code | c |
| Source | rdamedia |
| 338 ## - CARRIER TYPE | |
| Carrier type term | online resource |
| Carrier type code | cr |
| Source | rdacarrier |
| 490 1# - SERIES STATEMENT | |
| Series statement | Memoirs of the American Mathematical Society ; |
| Volume/sequential designation | v.245 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Chapter 1. Introduction -- 1.1. Convex preorders and cuspidal systems -- 1.2. Imaginary representations -- 1.3. Imaginary Schur-Weyl duality -- 1.4. Imaginary Howe and Ringel dualities -- 1.5. Gelfand-Graev words and representations -- 1.6. Example: type ₁⁽¹⁾ -- 1.7. Structure of the paper -- 1.8. Acknowledgements -- Chapter 2. Preliminaries -- 2.1. Partitions and compositions -- 2.2. Coset representatives -- 2.3. Schur algebras -- 2.4. Representation theory of Schur algebras -- 2.5. Induction and restriction for Schur algebras -- 2.6. Schur functors -- Chapter 3. Khovanov-Lauda-Rouquier algebras -- 3.1. Lie theoretic notation -- 3.2. The definition and first properties -- 3.3. Basic representation theory of _{\al} -- 3.4. Induction, coinduction, and duality for KLR algebras -- 3.5. Crystal operators and extremal words -- 3.6. Mackey Theorem -- 3.7. Convex preorders and root partitions -- 3.8. Cuspidal systems and standard modules -- 3.9. Colored imaginary tensor spaces -- Chapter 4. Imaginary Schur-Weyl duality -- 4.1. Imaginary tensor space and its parabolic analogue -- 4.2. Action of \Si_{ } on _{ } -- 4.3. Imaginary Schur algebras -- 4.4. Characteristic zero theory -- 4.5. Imaginary induction and restriction -- Chapter 5. Imaginary Howe duality -- 5.1. Gelfand-Graev modules -- 5.2. Imaginary symmetric, divided, and exterior powers -- 5.3. Parabolic analogues -- 5.4. Schur algebras as endomorphism algebras -- 5.5. Projective generator for imaginary Schur algebra -- Chapter 6. Morita equaivalence -- 6.1. Morita equivalence functors -- 6.2. Induction and Morita equivalence -- 6.3. Alternative definitions of standard modules -- 6.4. Base change -- 6.5. Ringel duality and double centralizer properties -- Chapter 7. On formal characters of imaginary modules -- 7.1. Weight multiplicities in \La^{\la^{\tr}}( _{ℎ}). |
| 505 8# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | 7.2. Gelfand-Graev words and shuffles -- 7.3. Gelfand-Graev fragment of the formal character of \Dede(\la) -- 7.4. Imaginary Jacobi-Trudy formula -- Chapter 8. Imaginary tensor space for non-simply-laced types -- 8.1. Minuscule representations for non-simply-laced types -- 8.2. The endomorphism ᵣ: _{ }→ _{ } for non-simply-laced types -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | 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. |
| 588 ## - SOURCE OF DESCRIPTION NOTE | |
| Source of description note | Description based on publisher supplied metadata and other sources. |
| 590 ## - LOCAL NOTE (RLIN) | |
| Local note | Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Duality theory (Mathematics). |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Muth, Robert. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Kleshchev, Alexander |
| Title | Imaginary Schur-Weyl Duality |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2017 |
| International Standard Book Number | 9781470422493 |
| 797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN) | |
| Corporate name or jurisdiction name as entry element | ProQuest (Firm) |
| 830 #0 - SERIES ADDED ENTRY--UNIFORM TITLE | |
| Uniform title | Memoirs of the American Mathematical Society |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908273">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=4908273</a> |
| Public note | Click to View |
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