Geometry and representation theory of symplectic singularities in the context of symplectic duality
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krylov-krvas-phd-mathematics-2024-thesis.pdf
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Thesis PDF
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1.44 MB
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Author(s)
Krylov, Vasily
Advisor(s)
Bezrukavnikov, Roman
Date Issued
May 2024
Publisher
Massachusetts Institute of Technology
Abstract
This thesis studies the geometry and representation theory of various symplectic resolutions of singularities from different perspectives. Specifically, following the ideas of Bellamy, Hilburn, Kamnitzer, Tingley, Webster, Weekes, and Yacobi, we establish a general approach to attack the Hikita-Nakajima conjecture and illustrate this approach in the example of ADHM spaces. We also study minimally supported representations of the quantizations of ADHM spaces and provide explicit formulas for their characters. Lastly, we describe the monodromy of eigenvalues of quantum multiplication operators for type A Nakajima quiver varieties by examining Bethe subalgebras in Yangians and linking their spectrum with Kirillov-Reshetikhin crystals.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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