On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic

In this thesis we prove the existence of Jordan Decomposition in D_G/k, the ring of invariant differential operators on a semisimple algebraic group over a field of positive characteristic, and its corollaries. In particular, we define the semisimple center of D_G/k, denoted by Z_s(D_G/k), as the set of semisimple elements of its center. Then we show that if $G$ is connected, the semisimple center Z_s(D_G/k) contains Z_s(D_G/k^(\nu)) for any positive interger $\nu$, where Z_s(D_G/k^(\nu)) is the ring of invariant differential operators on a Frobenius kernel derived from $G$.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Tian, Hongfei

Contributors dc:contributor

• Haboush, William J.
• Bergvelt, Maarten J.
• Yong, Alexander
• Nevins, Thomas A.

• Representation theory
• Positive characteristic
• Invariant differential operators
• Semisimple center

Statement dc:rights

• Copyright 2017 Hongfei Tian

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/99314

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F99314