Quiver Grassmannians of Extended Dynkin Type (Record no. 15197)
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| 000 -LEADER | |
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| fixed length control field | 04275nam a22004693i 4500 |
| 001 - CONTROL NUMBER | |
| control field | EBC5990837 |
| 003 - CONTROL NUMBER IDENTIFIER | |
| control field | MiAaPQ |
| 005 - DATE AND TIME OF LATEST TRANSACTION | |
| control field | 20240724114049.0 |
| 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 | 240724s2019 xx o ||||0 eng d |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| International Standard Book Number | 9781470453992 |
| Qualifying information | (electronic bk.) |
| 020 ## - INTERNATIONAL STANDARD BOOK NUMBER | |
| Canceled/invalid ISBN | 9781470436476 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (MiAaPQ)EBC5990837 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (Au-PeEL)EBL5990837 |
| 035 ## - SYSTEM CONTROL NUMBER | |
| System control number | (OCoLC)1130902668 |
| 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 | QA613.6 |
| Item number | .L67 2019 |
| 100 1# - MAIN ENTRY--PERSONAL NAME | |
| Personal name | Lorscheid, Oliver. |
| 245 10 - TITLE STATEMENT | |
| Title | Quiver Grassmannians of Extended Dynkin Type |
| Designation of section/part/series (SE) [OBSOLETE] | |
| -- | Part I : |
| Remainder of title | Schubert Systems and Decompositions into Affine Spaces. |
| 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 | 2019. |
| 264 #4 - PRODUCTION, PUBLICATION, DISTRIBUTION, MANUFACTURE, AND COPYRIGHT NOTICE | |
| Date of production, publication, distribution, manufacture, or copyright notice | ©2019. |
| 300 ## - PHYSICAL DESCRIPTION | |
| Extent | 1 online resource (90 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 Series ; |
| Volume/sequential designation | v.261 |
| 505 0# - FORMATTED CONTENTS NOTE | |
| Formatted contents note | Cover -- Title page -- Introduction -- Chapter 1. Background -- 1.1. Coefficient quiver -- 1.2. Schubert decompositions -- 1.3. Representations of Schubert cells -- Chapter 2. Schubert systems -- 2.1. The complete Schubert system -- 2.2. Partial Evaluations -- 2.3. Contradictory -states -- 2.4. Definition of -states -- 2.5. The reduced Schubert system -- 2.6. Computing -states -- 2.7. Solvable -states -- 2.8. Extremal edges -- 2.9. Patchwork solutions -- 2.10. Extremal paths -- Chapter 3. First applications -- 3.1. The Kronecker quiver -- 3.2. Dynkin quivers -- Chapter 4. Schubert decompositions for type ̃ _{ } -- 4.1. Contradictory of the first and of the second kind -- 4.2. Automorphisms of the Dynkin diagram -- 4.3. Bases for some indecomposable representations -- 4.4. The main theorem -- Chapter 5. Proof of Theorem 4.1 -- 5.1. Defect -1 -- Appendix A. Representations for quivers of type ̃ _{ } -- A.1. Reflections and Auslander-Reiten translates -- A.2. Indecomposable and exceptional representations -- A.3. The Auslander-Reiten quiver -- A.4. The tubes -- A.5. Roots -- A.6. The defect -- Appendix B. Bases for representations of type ̃ _{ } -- B.1. Defect -1 -- B.2. Defect -2 -- B.3. Positive defect -- B.4. Exceptional tubes of rank 2 -- B.5. Exceptional tubes of rank -2 -- B.6. Homogeneous tubes -- Bibliography -- Back Cover. |
| 520 ## - SUMMARY, ETC. | |
| Summary, etc. | Let Q be a quiver of extended Dynkin type \widetilde{D}_n. In this first of two papers, the authors show that the quiver Grassmannian \mathrm{Gr}_{underline{e}}(M) has a decomposition into affine spaces for every dimension vector underline{e} and every indecomposable representation M of defect -1 and defect 0, with the exception of the non-Schurian representations in homogeneous tubes. The authors characterize the affine spaces in terms of the combinatorics of a fixed coefficient quiver for M. The method of proof is to exhibit explicit equations for the Schubert cells of \mathrm{Gr}_{underline{e}}(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution the authors develop the theory of Schubert systems. In Part 2 of this pair of papers, they extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M. |
| 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 | Dynkin diagrams. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Grassmann manifolds. |
| 650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM | |
| Topical term or geographic name entry element | Mathematics. |
| 655 #4 - INDEX TERM--GENRE/FORM | |
| Genre/form data or focus term | Electronic books. |
| 700 1# - ADDED ENTRY--PERSONAL NAME | |
| Personal name | Weist, Thorsten. |
| 776 08 - ADDITIONAL PHYSICAL FORM ENTRY | |
| Relationship information | Print version: |
| Main entry heading | Lorscheid, Oliver |
| Title | Quiver Grassmannians of Extended Dynkin Type |
| Place, publisher, and date of publication | |
| -- | Part I: Schubert Systems and Decompositions into Affine Spaces |
| Place, publisher, and date of publication | Providence : American Mathematical Society,c2019 |
| International Standard Book Number | 9781470436476 |
| 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 Series |
| 856 40 - ELECTRONIC LOCATION AND ACCESS | |
| Uniform Resource Identifier | <a href="https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5990837">https://ebookcentral.proquest.com/lib/orpp/detail.action?docID=5990837</a> |
| Public note | Click to View |
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