£81.83

Quiver Grassmannians of Extended Dynkin Type $D$: Part I: Schubert Systems and Decompositions Into Affine Spaces: 261 (Memoirs of the American Mathematical Society)

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£82 today · usual range £72–£84 · best ever £72

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Description
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 $M$.

Product Specifications
Format
paperback
ASIN
1470436477
Category
Books > Subjects > Science, Nature & Maths > Mathematics > Algebra
Domain
Amazon UK
Release Date
30 October 2019
Listed Since
23 July 2019

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