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Title:On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution
Author(s):Im, Mee Seong
Director of Research:Nevins, Thomas A.
Doctoral Committee Chair(s):Kedem, Rinat
Doctoral Committee Member(s):Nevins, Thomas A.; Bergvelt, Maarten J.; Schenck, Henry K.
Department / Program:Mathematics
Discipline:Mathematics
Degree Granting Institution:University of Illinois at Urbana-Champaign
Degree:Ph.D.
Genre:Dissertation
Subject(s):Algebraic geometry
representation theory
quiver varieties
filtered quiver variety
quiver flag variety
semi-invariant polynomials
invariant subring
Derksen-Weyman
Domokos-Zubkov
Schofield-van den Bergh
ADE-Dynkin quivers
affine Dynkin quivers
quivers with at most two pathways between any two vertices
filtration of vector spaces
classical invariant theory
the Hamiltonian reduction of the cotangent bundle of the enhanced Grothendieck-Springer resolution
almost-commuting varieties
affine quotient
Abstract:We introduce the notion of filtered representations of quivers, which is related to usual quiver representations, but is a systematic generalization of conjugacy classes of $n\times n$ matrices to (block) upper triangular matrices up to conjugation by invertible (block) upper triangular matrices. With this notion in mind, we describe the ring of invariant polynomials for interesting families of quivers, namely, finite $ADE$-Dynkin quivers and affine type $\widetilde{A}$-Dynkin quivers. We then study their relation to an important and fundamental object in representation theory called the Grothendieck-Springer resolution, and we conclude by stating several conjectures, suggesting further research.
Issue Date:2014-05-30
URI:http://hdl.handle.net/2142/49392
Rights Information:Copyright 2014 Mee Seong Im
Date Available in IDEALS:2014-05-30
Date Deposited:2014-05


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