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University of Illinois – Urbana-Champaign

1. Sun, Hao. W-operators and generating functions of hurwitz numbers.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101336

► This thesis is motivated by the W-operators introduced by Mironov et al. We prove that the W-operators are generalizations of the cut-and-join operator studied by…
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Subjects/Keywords: W-operator; Hurwitz number; Cut-and-join operator

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Sun, H. (2018). W-operators and generating functions of hurwitz numbers. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101336

Chicago Manual of Style (16^{th} Edition):

Sun, Hao. “W-operators and generating functions of hurwitz numbers.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 29, 2020. http://hdl.handle.net/2142/101336.

MLA Handbook (7^{th} Edition):

Sun, Hao. “W-operators and generating functions of hurwitz numbers.” 2018. Web. 29 Sep 2020.

Vancouver:

Sun H. W-operators and generating functions of hurwitz numbers. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/2142/101336.

Council of Science Editors:

Sun H. W-operators and generating functions of hurwitz numbers. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101336

University of Illinois – Urbana-Champaign

2. Pechenik, Oliver A. K-theoretic Schubert calculus and applications.

Degree: PhD, Mathematics, 2016, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/92740

► A central result in algebraic combinatorics is the Littlewood-Richardson rule that governs products in the cohomology of Grassmannians. A major theme of the modern Schubert…
(more)

Subjects/Keywords: Schubert calculus; K-theory; genomic tableau; cyclic sieving; homomesy; plane partition; resonance; doppelganger

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Pechenik, O. A. (2016). K-theoretic Schubert calculus and applications. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/92740

Chicago Manual of Style (16^{th} Edition):

Pechenik, Oliver A. “K-theoretic Schubert calculus and applications.” 2016. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 29, 2020. http://hdl.handle.net/2142/92740.

MLA Handbook (7^{th} Edition):

Pechenik, Oliver A. “K-theoretic Schubert calculus and applications.” 2016. Web. 29 Sep 2020.

Vancouver:

Pechenik OA. K-theoretic Schubert calculus and applications. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2016. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/2142/92740.

Council of Science Editors:

Pechenik OA. K-theoretic Schubert calculus and applications. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2016. Available from: http://hdl.handle.net/2142/92740

University of Illinois – Urbana-Champaign

3. Vichitkunakorn, Panupong. Cluster algebras and discrete integrable systems.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/97314

► This dissertation presents connections between cluster algebras and discrete integrable systems, especially T-systems and their specializations/generalizations. We give connections between the T-system or the octahedron…
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Subjects/Keywords: Cluster algebras; Discrete integrable systems

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Vichitkunakorn, P. (2017). Cluster algebras and discrete integrable systems. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/97314

Chicago Manual of Style (16^{th} Edition):

Vichitkunakorn, Panupong. “Cluster algebras and discrete integrable systems.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 29, 2020. http://hdl.handle.net/2142/97314.

MLA Handbook (7^{th} Edition):

Vichitkunakorn, Panupong. “Cluster algebras and discrete integrable systems.” 2017. Web. 29 Sep 2020.

Vancouver:

Vichitkunakorn P. Cluster algebras and discrete integrable systems. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/2142/97314.

Council of Science Editors:

Vichitkunakorn P. Cluster algebras and discrete integrable systems. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/97314

4. Weigandt, Anna. Prism tableaux and alternating sign matrices.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101525

► A. Lascoux and M.-P. Schutzenberger introduced Schubert polynomials to study the cohomology ring of the complete flag variety Fl(C^n). Each Schubert polynomial corresponds to the…
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Subjects/Keywords: Schubert polynomials; Alternating sign matrices; Durfee; Prism tableaux

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Weigandt, A. (2018). Prism tableaux and alternating sign matrices. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101525

Chicago Manual of Style (16^{th} Edition):

Weigandt, Anna. “Prism tableaux and alternating sign matrices.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 29, 2020. http://hdl.handle.net/2142/101525.

MLA Handbook (7^{th} Edition):

Weigandt, Anna. “Prism tableaux and alternating sign matrices.” 2018. Web. 29 Sep 2020.

Vancouver:

Weigandt A. Prism tableaux and alternating sign matrices. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/2142/101525.

Council of Science Editors:

Weigandt A. Prism tableaux and alternating sign matrices. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101525

5. Monical, Cara. Polynomials in algebraic combinatorics.

Degree: PhD, Mathematics, 2018, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/101462

► A long-standing theme in algebraic combinatorics is to study bases of the rings of symmetric functions, quasisymmetric functions, and polynomials. Classically, these bases are homogeneous…
(more)

Subjects/Keywords: K-theoretic algebraic combinatorics; skyline fillings; Newton polytopes

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Monical, C. (2018). Polynomials in algebraic combinatorics. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/101462

Chicago Manual of Style (16^{th} Edition):

Monical, Cara. “Polynomials in algebraic combinatorics.” 2018. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 29, 2020. http://hdl.handle.net/2142/101462.

MLA Handbook (7^{th} Edition):

Monical, Cara. “Polynomials in algebraic combinatorics.” 2018. Web. 29 Sep 2020.

Vancouver:

Monical C. Polynomials in algebraic combinatorics. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2018. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/2142/101462.

Council of Science Editors:

Monical C. Polynomials in algebraic combinatorics. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2018. Available from: http://hdl.handle.net/2142/101462

6. Turmunkh, Bolor. Nakajima's (Q, T)-characters as quantum cluster variables.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98093

► Nakajima introduced a t-deformation of q-characters, (q,t)-characters for short, and their twisted multiplication through the geometry of quiver varieties. The Nakajima (q, t)-characters of Kirillov-Reshetikhin…
(more)

Subjects/Keywords: T-system; Nakajima (q,t)-characters; Quantum cluster algebra

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Turmunkh, B. (2017). Nakajima's (Q, T)-characters as quantum cluster variables. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98093

Chicago Manual of Style (16^{th} Edition):

Turmunkh, Bolor. “Nakajima's (Q, T)-characters as quantum cluster variables.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 29, 2020. http://hdl.handle.net/2142/98093.

MLA Handbook (7^{th} Edition):

Turmunkh, Bolor. “Nakajima's (Q, T)-characters as quantum cluster variables.” 2017. Web. 29 Sep 2020.

Vancouver:

Turmunkh B. Nakajima's (Q, T)-characters as quantum cluster variables. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/2142/98093.

Council of Science Editors:

Turmunkh B. Nakajima's (Q, T)-characters as quantum cluster variables. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98093

7. Addabbo, Darlayne. Q-systems and generalizations in representation theory.

Degree: PhD, Mathematics, 2017, University of Illinois – Urbana-Champaign

URL: http://hdl.handle.net/2142/98257

► We study tau-functions given as matrix elements for the action of loop groups, GL_{n}̂ on n-component fermionic Fock space. In the simplest case, n=2, the…
(more)

Subjects/Keywords: Q-systems; Representation theory; Integrable systems; Box and ball systems

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} Edition):

Addabbo, D. (2017). Q-systems and generalizations in representation theory. (Doctoral Dissertation). University of Illinois – Urbana-Champaign. Retrieved from http://hdl.handle.net/2142/98257

Chicago Manual of Style (16^{th} Edition):

Addabbo, Darlayne. “Q-systems and generalizations in representation theory.” 2017. Doctoral Dissertation, University of Illinois – Urbana-Champaign. Accessed September 29, 2020. http://hdl.handle.net/2142/98257.

MLA Handbook (7^{th} Edition):

Addabbo, Darlayne. “Q-systems and generalizations in representation theory.” 2017. Web. 29 Sep 2020.

Vancouver:

Addabbo D. Q-systems and generalizations in representation theory. [Internet] [Doctoral dissertation]. University of Illinois – Urbana-Champaign; 2017. [cited 2020 Sep 29]. Available from: http://hdl.handle.net/2142/98257.

Council of Science Editors:

Addabbo D. Q-systems and generalizations in representation theory. [Doctoral Dissertation]. University of Illinois – Urbana-Champaign; 2017. Available from: http://hdl.handle.net/2142/98257

8. 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

URL: http://hdl.handle.net/2142/49392

► 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…
(more)

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

Record Details Similar Records

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6^{th} 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 (16^{th} 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 September 29, 2020. http://hdl.handle.net/2142/49392.

MLA Handbook (7^{th} Edition):

Im, Mee Seong. “On semi-invariants of filtered representations of quivers and the cotangent bundle of the enhanced Grothendieck-Springer resolution.” 2014. Web. 29 Sep 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 Sep 29]. 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