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1. Im, Mee Seong. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.

Degree: PhD, 0439, 2014, University of Illinois – Urbana-Champaign

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 ×  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. Advisors/Committee Members: Nevins, Thomas A. (advisor), Kedem, Rinat (Committee Chair), Nevins, Thomas A. (committee member), Bergvelt, Maarten J. (committee member), Schenck, Henry K. (committee member).

Subjects/Keywords: 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

…Schur algebras as a quotient of a convolution algebra in the study of quiver varieties via a… …GLβi (C) acts via change i∈Q0 of basis in Cβi . We say a quiver is an (affine… …x29; Dynkin quiver if the underlying graph has the structure of an (affine) Dynkin… …presented here, consider ADE-Dynkin quivers and affine type Ar -Dynkin quivers. If Q if an ADE… …χ 0 2. If Q is an affine type Ar -Dynkin quiver and β = (n, . . . , n) ∈ ZQ ≥0… 

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APA (6th Edition):

Im, M. S. (2014). On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/49392

Chicago Manual of Style (16th Edition):

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed August 05, 2020. http://hdl.handle.net/2142/49392.

MLA Handbook (7th Edition):

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Web. 05 Aug 2020.

Vancouver:

Im MS. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2014. [cited 2020 Aug 05]. Available from: http://hdl.handle.net/2142/49392.

Council of Science Editors:

Im MS. On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2014. Available from: http://hdl.handle.net/2142/49392

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