| Description |
1 online resource (90 pages) |
| Series |
Memoirs of the American Mathematical Society Ser. ; v. 261 |
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Memoirs of the American Mathematical Society Ser
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| Contents |
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 |
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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 ̃ _{ } |
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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 |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 77-78) |
| Notes |
Print version record |
| Subject |
Geometry, Algebraic.
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Geometría algebraica
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Geometry, Algebraic
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| Form |
Electronic book
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| Author |
Weist, Thorsten
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| ISBN |
9781470453992 |
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1470453991 |
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