Degree Type

Creative Component

Semester of Graduation

Summer 2021

Department

Mathematics

First Major Professor

Jonas Hartwig

Degree(s)

Master of Science (MS)

Major(s)

Mathematics

Abstract

The McKay correspondence states that there is a bijection between the McKay graphs of finite subgroups of $SU_2$ and Dynkin diagrams in the $ADE$ classification system of simply laced Lie algebras. We investigate this correspondence by finding the finite subgroups of $SU_2$ and explicitly constructing the McKay graph corresponding to each group. We then view these groups from the lens of algebraic geometry and go through the blow-up procedure for the corresponding Kleinian singularities to demonstrate that the blow-up graph, quite remarkably, yields another way to obtain the Dynkin diagrams.

Copyright Owner

Hobart, Matthew

File Format

PDF

Embargo Period (admin only)

7-6-2021

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