Quiver Grassmannians for the Bott-Samelson Resolution of Type A Schubert Varieties

IF 0.6 4区数学 Q3 MATHEMATICS

Algebras and Representation Theory Pub Date : 2025-08-11 DOI:10.1007/s10468-025-10356-3

Giulia Iezzi

引用次数: 0

Abstract

We realise the Bott-Samelson resolutions of type A Schubert varieties as quiver Grassmannians. In order to explicitly describe this isomorphism, we introduce the notion of a geometrically compatible decomposition for any permutation in the symmetric group \(S_n\). For smooth type A Schubert varieties, we identify a suitable dimension vector such that the corresponding quiver Grassmannian is isomorphic to the Schubert variety. To obtain these isomorphisms, we construct a special quiver with relations and investigate two classes of quiver Grassmannians for this quiver.

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舒伯特A型品种botsamelson分解的Quiver Grassmannians

我们认识到A型舒伯特品种的波特-萨缪尔森分辨率为颤抖的格拉斯曼分辨率。为了明确地描述这种同构，我们引入了对对称群\(S_n\)中任意置换的几何相容分解的概念。对于光滑A型Schubert变种，我们确定了一个合适的维向量，使得相应的抖动格拉斯曼算子与Schubert变种同构。为了得到这些同构，我们构造了一个特殊的带关系的颤振，并研究了该类颤振的两类格拉斯曼算子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Algebras and Representation Theory 数学-数学

CiteScore

1.30

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebras and Representation Theory features carefully refereed papers relating, in its broadest sense, to the structure and representation theory of algebras, including Lie algebras and superalgebras, rings of differential operators, group rings and algebras, C*-algebras and Hopf algebras, with particular emphasis on quantum groups. The journal contains high level, significant and original research papers, as well as expository survey papers written by specialists who present the state-of-the-art of well-defined subjects or subdomains. Occasionally, special issues on specific subjects are published as well, the latter allowing specialists and non-specialists to quickly get acquainted with new developments and topics within the field of rings, algebras and their applications.