Date of Award
Spring 2024
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Loseu, Ivan
Abstract
This dissertation is devoted to the study of two topics on quantizations of quiver varieties, combining the works of the author during his PhD. The first topic concerns graded Poisson deformations of quiver varieties. We provide algorithms to compute the Namikawa-Weyl group of the affinization of a smooth Nakajima quiver variety from the quiver combinatorial data. This extends a result of [MN19] for quiver varieties associated to Dynkin quivers. The second topic concerns the classification of Harish-Chandra bimodules over the quantizations of flower quiver varieties, i.e. the quiver with one vertex and ≥ 2 edge-loops. We show that if the dimension vector is n, then there are n! minimally supported simple Harish-Chandra bimodules for integral quantization parameters that are large enough or small enough, and there are none for other quantization parameters. The main tool used for this classification is an enhanced version of the restriction functor introduced in [Los11] and [Los12a].
Recommended Citation
Wu, Yaochen, "Two Topics on Quantizations of Quiver Varieties" (2024). Yale Graduate School of Arts and Sciences Dissertations. 1386.
https://elischolar.library.yale.edu/gsas_dissertations/1386
