02782nam 2200529 450 991081603300332120200106153957.01-4704-5399-1(CKB)4940000000160190(MiAaPQ)EBC5990837(RPAM)21564451(PPN)242522386(EXLCZ)99494000000016019020200106h20192019 uy| 0engurcnu||||||||rdacontentrdamediardacarrierQuiver grassmannians of extended Dynkin type DPart ISchubert systems and decompositions into affien spaces /Oliver Lorscheid, Thorsten WeistProvidence, RI :American Mathematical Society,[2019]©20191 online resource (90 pages) illustrationsMemoirs of the American Mathematical Society,0065-9266 ;September 2019, volume 261, number 12581-4704-3647-7 Includes bibliographical references.Background -- Schubert systems -- First applications -- Schubert decompositions for type Dn -- Proof of Theorem 4.1."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"--Provided by publisher.Memoirs of the American Mathematical Society ;vol. 261, no. 1258.Schubert systems and decompositions into affine spacesDynkin diagramsGrassmann manifoldsMathematicsDynkin diagrams.Grassmann manifolds.Mathematics.516.3/5213F6014F4514M1514N1516G2005E1014M1716G60mscLorscheid Oliver1703551Weist ThorstenMiAaPQMiAaPQMiAaPQBOOK9910816033003321Quiver grassmannians of extended Dynkin type D4088839UNINA