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 Title: On the center of the ring of invariant differential operators on semisimple groups over fields of positive characteristic Author(s): Tian, Hongfei Director of Research: Haboush, William J Doctoral Committee Chair(s): Bergvelt, Maarten J Doctoral Committee Member(s): Yong, Alexander; Nevins, Thomas A Department / Program: Mathematics Discipline: Mathematics Degree Granting Institution: University of Illinois at Urbana-Champaign Degree: Ph.D. Genre: Dissertation Subject(s): Representation theory Positive characteristic Invariant differential operators Semisimple center Abstract: 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 $G$. Issue Date: 2017-10-30 Type: Text URI: http://hdl.handle.net/2142/99314 Rights Information: Copyright 2017 Hongfei Tian Date Available in IDEALS: 2018-03-13 Date Deposited: 2017-12
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