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Die folgenden Informationen sind noch nicht freigegeben und deshalb unverbindlich: Representation Theory of the Symmetric Group SemesterWiSe 2026 / 27 Lecturer Himanshu Shukla (FIDS) Type of course (Veranstaltungsart) Seminar German title Representation Theory of the Symmetric Group Contents For this course we will mainly follow the book of Bruce E. Sagan " The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions" available at this Springer-Verlag link. In addition, the book of Serre on the representation theory of finite groups, which could be found herewill be helpful. The aim of this seminar course is to dive deeper into the representation of theory of symmetric groups and see some implications in Theoretical Computer Science. We will quickly recall some important results and definitions from the representation theory of finite groups and characters theory in the beginning and specialize to the case of symmetric groups, therefore some acquaintance with group theory, linear algebra and abstract algebra is required. Furthermore, acquaintance with the representation theory of finite groups will be helpful but not required. 1) Recall: - Group representations - Group algebras and modules - Maschke's theorem - Morphisms of representations - Schur's lemma - Class functions - Characters - Inner-product of characters - Irreducible representations and characters correspondence - Group algebra decomposition - Tensor products 2) Representations of S_n: - Young tableaux - Specht modules - Garnir elements and Young's natural representation - Young's rule 3) Algorithms: - Robinson-Schensted algorithm - Schuetzenberger's Jeu De Tarquin - Dual equivalence - Hook formula - Littlewood-Richardson rule - Murnaghan-Nakayama rule. Comment Not all the results will be stated with proofs. However, we will introduce the key ideas required to state and understand the statement and some of the implications of such results. The idea is to get acquainted with the theory and the tools used in the representation theory of the symmetric groups. Recommended previous knowledge For this course we will mainly follow the book of Bruce E. Sagan " The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions". In addition, the book of Serre "Linear Representations of finite groups" will be helpful. The aim of this seminar course is to dive deeper into the representation of theory of symmetric groups and see some implications in Theoretical Computer Science. We will quickly recall some important results and definitions from the representation theory of finite groups and characters theory in the beginning and specialize to the case of symmetric groups, therefore some acquaintance with group theory, linear algebra and abstract algebra is required. Furthermore, acquaintance with the representation theory of finite groups will be helpful but not required. Time/Date Wed 14-16 Location PHY 9.1.11 Course homepage https://elearning.uni-regensburg.de/course/view.php?id=76386 (Disclaimer: Dieser Link wurde automatisch erzeugt und ist evtl. extern) Registration
MV, Wahlbereich ECTS 6 |