Thesis advisor: Solomon Friedberg / Kazhdan and Patterson constructed generalized theta representations on covers of general linear groups as multi-residues of the Borel Eisenstein series. For the double covers, these representations and their (degenerate-type) unique models were used by Bump and Ginzburg in the Rankin-Selberg constructions of the symmetric square L-functions for GL(r). In this thesis, we study two other types of models that the theta representations may support. We first discuss semi-Whittaker models, which generalize the models used in the work of Bump and Ginzburg. Secondly, we determine the unipotent orbits attached to theta functions, in the sense of Ginzburg. We also determine the covers for which these models are unique. We also describe briefly some applications of these unique models in Rankin-Selberg integrals for covering groups. / Thesis (PhD) — Boston College, 2017. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

Thesis advisor: Solomon Friedberg / We study the generalized theta lifting between the double covers of split special orthogonal groups, which uses the non-minimal theta representations constructed by Bump, Friedberg and Ginzburg. We focus on the theta liftings of non-generic representations and make a conjecture that gives an upper bound of the first non-zero occurrence of the liftings, depending only on the unipotent orbit. We prove both global and local results that support the conjecture. / Thesis (PhD) — Boston College, 2021. / Submitted to: Boston College. Graduate School of Arts and Sciences. / Discipline: Mathematics.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第25092号 / 理博第4999号 / 新制||理||1714(附属図書館) / 京都大学大学院理学研究科数学・数理解析専攻 / (主査)教授 池田 保, 教授 市野 篤史, 准教授 伊藤 哲史 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM