Softcover ISBN:  9781470436476 
Product Code:  MEMO/261/1258 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470453992 
Product Code:  MEMO/261/1258.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470436476 
eBook: ISBN:  9781470453992 
Product Code:  MEMO/261/1258.B 
List Price:  $162.00 $121.50 
MAA Member Price:  $145.80 $109.35 
AMS Member Price:  $97.20 $72.90 
Softcover ISBN:  9781470436476 
Product Code:  MEMO/261/1258 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
eBook ISBN:  9781470453992 
Product Code:  MEMO/261/1258.E 
List Price:  $81.00 
MAA Member Price:  $72.90 
AMS Member Price:  $48.60 
Softcover ISBN:  9781470436476 
eBook ISBN:  9781470453992 
Product Code:  MEMO/261/1258.B 
List Price:  $162.00 $121.50 
MAA Member Price:  $145.80 $109.35 
AMS Member Price:  $97.20 $72.90 

Book DetailsMemoirs of the American Mathematical SocietyVolume: 261; 2019; 78 ppMSC: Primary 13; 14; 16; Secondary 05
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 nonSchurian 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 \(M\).

Table of Contents

Chapters

Introduction

1. Background

2. Schubert systems

3. First applications

4. Schubert decompositions for type $\widetilde D_n$

5. Proof of Theorem 4.1

A. Representations for quivers of type $\widetilde D_n$

B. Bases for representations of type $\widetilde D_n$


Additional Material

RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Requests
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 nonSchurian 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 \(M\).

Chapters

Introduction

1. Background

2. Schubert systems

3. First applications

4. Schubert decompositions for type $\widetilde D_n$

5. Proof of Theorem 4.1

A. Representations for quivers of type $\widetilde D_n$

B. Bases for representations of type $\widetilde D_n$