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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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