Flatness of the commutator map on special linear groups

This thesis contributes to the study of the fibers of the commutator map on special linear groups in characteristic zero. Specifically, we show that the fibers over non-central elements all have the same dimension. Also we explain that the fibers over central elements can be of larger dimension and compute how large. We use the character tables of finite general linear groups constructed by J.A. Green to count solutions to the commutator equation [$x,y$] = $g$ over finite fields and use algebraic geometry to go from characteristic $p$ to characteristic 0. To deal with fibers over central elements, we compute the orbits of the conjugation action of GL_n on these fibers.

Grantor dc:publisher

[Bloomington, Ind.] : Indiana University

Year dc:date.issued

2018

Author dc:creator

• Lu, Zhipeng

Advisor dc:contributor.advisor

• Larsen, Michael

• algebraic geometry
• character estimates
• commutator

Language dc:language.iso

en

Handle dc:identifier.uri

https://hdl.handle.net/2022/22413

OAI identifier oai:identifier

oai:scholarworks.iu.edu:2022/22413