Geometry and representation theory of symplectic singularities in the context of symplectic duality

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.

Name thesis:degree_name

Doctoral

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2024

Author dc:creator

• Krylov, Vasily

Advisor dc:contributor.advisor

• Bezrukavnikov, Roman

Statement dc:rights

• In Copyright - Educational Use Permitted
• Copyright retained by author(s)

Licence dc:rights.uri

• https://rightsstatements.org/page/InC-EDU/1.0/

Handle dc:identifier.uri

https://hdl.handle.net/1721.1/155322

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/155322