Dokument: On the Representations of Quasi-semisimple Profinite Groups, Compact p-adic Analytic Groups, and Baumslag-Solitar Groups

Titel:	On the Representations of Quasi-semisimple Profinite Groups, Compact p-adic Analytic Groups, and Baumslag-Solitar Groups
URL für Lesezeichen:	https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=68237
URN (NBN):	urn:nbn:de:hbz:061-20250203-084400-2
Kollektion:	Dissertationen
Sprache:	Englisch
Dokumententyp:	Wissenschaftliche Abschlussarbeiten » Dissertation
Medientyp:	Text
Autor:	Piccolo, Margherita [Autor]
Dateien:	[Dateien anzeigen] Adobe PDF [Details] 1,01 MB in einer Datei [ZIP-Datei erzeugen] Dateien vom 28.01.2025 / geändert 28.01.2025
Beitragende:	Prof. Dr. Klopsch, Benjamin [Gutachter] Prof. Dr. Späth, Britta [Gutachter]
Dewey Dezimal-Klassifikation:	500 Naturwissenschaften und Mathematik » 510 Mathematik
Beschreibung:	This dissertation is cumulative; it consists of three parts that deal with representation growth of infinite groups. We study the asymptotic behaviour of representations in three different contexts. Namely, for quasi-semisimple profinite groups, compact p-adic analytic groups, and Baumslag-Solitar groups. In the first part of the thesis, we give some preliminaries that will help to understand the subject of the following chapters. In the second part of the thesis, we examine quasi-semisimple profinite groups. Notably, we prove that every positive real number occurs as the abscissa of convergence for a suitable group within this class. The third part of the thesis focuses on the representation zeta functions of principal congruence subgroups and certain extensions of the group SL_2^m(O), the m-th principal congruence subgroup of the special linear group of degree 2 over a compact discrete valuation ring O of characteristic 0 and residue characteristic p, for permissible m. We show that the considered zeta functions have the zeta function of SL_2^m(O) as a factor. In the fourth and final part, we address Baumslag-Solitar groups, investigating their absolutely irreducible representations over finite fields. The primary outcome is the enumeration and description of absolutely irreducible representations of dimension n for a Baumslag-Solitar group BS(x, y) with coprime parameters.
Lizenz:	Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz
Fachbereich / Einrichtung:	Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Algebra und Zahlentheorie
Dokument erstellt am:	03.02.2025
Dateien geändert am:	03.02.2025
Promotionsantrag am:	18.07.2024
Datum der Promotion:	25.09.2024