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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
Degree Granting Institution:University of Illinois at Urbana-Champaign
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
Rights Information:Copyright 2017 Hongfei Tian
Date Available in IDEALS:2018-03-13
Date Deposited:2017-12

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