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Title:Stratifications of representations and cyclic quivers
Author(s):Ochoa de Alaiza Gracia, Itziar
Director of Research:Nevins, Thomas
Doctoral Committee Chair(s):Loja Fernandes, Rui
Doctoral Committee Member(s):Yong, Alexander; Dodd, Christopher
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Representations, quivers.
Abstract:Given an algebraic variety $X$ with an action of a reductive group $G$, geometric invariant theory splits $X$ as the disjoint union $X=X^{ss}\sqcup X^{un}$ of the semistable and unstable locus. The Kirwan-Ness stratification refines $X$ even more by describing $X^{un}$ as a disjoint union of strata $X^{un}=\displaystyle\sqcup_{\beta\in\textsf{KN}} S_\beta$ detemined by 1-parameter subgroups $\beta$. In this thesis we study the 1-parameter subgroups that determine the Kirwan-Ness stratifications of representations. We will describe an algorithm that finds the $\beta$'s and we show that such algorithm can be simplified when our space is of the form $T^*V$ where $V$ is a vector space. We go on to investigate more deeply the 1-parameter subgroups in the case of the space of representations $\text{Rep}(Q,v)$ of a cyclic quiver $Q$.
Issue Date:2018-07-06
Type:Text
URI:http://hdl.handle.net/2142/101520
Rights Information:Copyright 2018 by Itziar Ochoa de Alaiza Gracia. All rights reserved.
Date Available in IDEALS:2018-09-27
Date Deposited:2018-08


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