Representation theory of unipotent linear algebraic groups and a generalized Kirillov theory for a class of nilpotent groups [Elektronische Ressource] / vorgelegt von Helma Klüver

Helma C. Kluver¨Representation theory ofunipotent linear algebraic groupsanda generalized Kirillov theory fora class of nilpotent groups2006MathematikDissertationsthemaRepresentation theory ofunipotent linear algebraic groupsanda generalized Kirillov theory fora class of nilpotent groupsInaugural-Dissertationzur Erlangung des Doktorgradesder Naturwissenschaften im FachbereichMathematik und Informatikder Mathematisch-Naturwissenschaftlichen Fakultat¨der Westfalischen Wilhelms-Universitat Munster¨ ¨ ¨vorgelegt vonHelma Kluver¨aus Neumunster¨-2006-Dekan: Prof. Dr. Dr. h.c. Joachim CuntzErster Gutachter: Prof. Dr. Siegfried EchterhoffZweiter Gutachter: Prof. Dr. Markus ReinekeTag der mu¨ndlichen Pru¨fung: 26.01.07Tag der Promotion: 26.01.07AbstractThis thesis is concerned with two different subjects in the field of representationtheory of nilpotent locally compact groups. The first part deals with the structuretheory of abelian unipotent linear algebraic groups over a local field K of charac-teristic p, which are treated as abstract topological groups. The finite-dimensionalWitt groups over K form a large class of these groups.The first main result is that every such Witt group,W (K), can be decomposed intona discrete and a compact part, each being the dual of the other. This implies thatthe topological group W (K) is isomorphic to its dual group, i.e., to its group ofncharacters.