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Record Nr. |
UNINA9910816033003321 |
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Autore |
Lorscheid Oliver |
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Titolo |
Quiver grassmannians of extended Dynkin type D . Part I Schubert systems and decompositions into affien spaces / / Oliver Lorscheid, Thorsten Weist |
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Pubbl/distr/stampa |
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Providence, RI : , : American Mathematical Society, , [2019] |
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©2019 |
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ISBN |
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Descrizione fisica |
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1 online resource (90 pages) : illustrations |
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Collana |
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Memoirs of the American Mathematical Society, , 0065-9266 ; ; September 2019, volume 261, number 1258 |
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Classificazione |
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13F6014F4514M1514N1516G2005E1014M1716G60 |
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Disciplina |
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Soggetti |
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Dynkin diagrams |
Grassmann manifolds |
Mathematics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di bibliografia |
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Includes bibliographical references. |
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Nota di contenuto |
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Background -- Schubert systems -- First applications -- Schubert decompositions for type Dn -- Proof of Theorem 4.1. |
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Sommario/riassunto |
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"Let Q be a quiver of extended Dynkin type Dn. In this first of two papers, we show that the quiver Grassmannian Gre(M) has a decomposition into affine spaces for every dimension vector e and every indecomposable representation M of defect -1 and defect 0, with exception of the non-Schurian representations in homogeneous tubes. We 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 Gre(M) and to solve this system of equations successively in linear terms. This leads to an intricate combinatorial problem, for whose solution we develop the theory of Schubert systems. In Part 2 of this pair of papers, we extend the result of this paper to all indecomposable representations M of Q and determine explicit formulae for the F-polynomial of M"-- |
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