Schubert systems and decompositions into affine spaces
著者
書誌事項
Schubert systems and decompositions into affine spaces
（Memoirs of the American Mathematical Society, no. 1258 . Quiver Grassmannians of extended Dynkin type D / Oliver Lorscheid,
American Mathematical Society, c2019
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注記
"September 2019, volume 261, number 1258 (second of 7 numbers)"
Includes bibliographical reference (p. 77-78)
内容説明・目次
内容説明
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 $M$.
目次
Introduction
Background
Schubert systems
First applications
Schubert decompositions for type $\widetilde{D}_n$
Proof of Theorem 4.1
Appendix A. Representations for quivers of type $\widetilde{D}_n$
Appendix B. Bases for representations of type $\widetilde{D}_n$
Bibliography.
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