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2014-05-30T16:41:46Z 2014-05-30T16:41:46Z 2014-05 2014-05-30T16:41:46Z Schenck, Henry K. Im, Mee Seong Nevins, Thomas A. Kedem, Rinat Nevins, Thomas A. Bergvelt, Maarten J. 2014-05 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. Item withdrawn by Mark Zulauf (zulauf@illinois.edu) on 2014-04-18T13:41:19Z Item was in collections: University of Illinois Theses & Dissertations (ID: 1) No. of bitstreams: 1 Im_MeeSeong.pdf: 1112913 bytes, checksum: 8bc94888423425498f92f49e5709a1ce (MD5) Made available in DSpace on 2014-05-30T16:41:46Z (GMT). No. of bitstreams: 2 Mee Seong_Im.pdf: 1112913 bytes, checksum: 8bc94888423425498f92f49e5709a1ce (MD5) license.txt: 4058 bytes, checksum: ef56fdb200ab46b3d2d21b5b5e0b8eeb (MD5) http://hdl.handle.net/2142/49392 en Copyright 2014 Mee Seong Im 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 On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution text Mathematics 1257 Mathematics 0439 University of Illinois at Urbana-Champaign Dissertation Ph.D. PHD:Mathematics -UIUC 10KS0439PHD