Quiver grassmannians of extended Dynkin type D. Part I, Schubert systems and decompositions into affien spaces / Oliver Lorscheid, Thorsten Weist.

Format:

Book

Author/Creator:

Lorscheid, Oliver, author.

Weist, Thorsten, author.

Series:

Memoirs of the American Mathematical Society ; vol. 261, no. 1258.

Memoirs of the American Mathematical Society, 0065-9266 ; September 2019, volume 261, number 1258

Language:

English

Subjects (All):

Dynkin diagrams.

Grassmann manifolds.

Mathematics.

Physical Description:

1 online resource (90 pages) : illustrations.

Edition:

1st ed.

Other Title:

Schubert systems and decompositions into affine spaces

Place of Publication:

Providence, RI : American Mathematical Society, [2019]

Summary:

"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.

Contents:

Background

Schubert systems

First applications

Schubert decompositions for type Dn

Proof of Theorem 4.1.

Notes:

Description based on online resource; title from PDF title page (ebrary, viewed January 6, 2020).

Includes bibliographical references.

ISBN:

1-4704-5399-1