Contact: jonas [dot] hetz [at] rwth-aachen [dot] de

Weekly Meetings (SoSe 2024): Thursdays, 14:30 - 16:00 in Seminarraum 103 of the LfAZ at RWTH Aachen

Prerequisites:

Standard undergraduate level courses on (linear) algebra. Some prior knowledge on ordinary representation/character theory may be useful, but should not be strictly necessary.

Webb, P., A course in finite group representation theory, Cambridge Studies in Advanced Mathematics, 161. Cambridge University Press, Cambridge, 2016.

Description and Format:

This Reading Group is meant as a venue for (graduate) students and postdocs in the chairs of algebra, number theory and representation theory to study and learn through reading some specified material followed by weekly moderated collaboration sessions on the newly acquired knowledge. This will typically include the discussion of previously selected problems/exercises on the topic.

Further Reading:

Navarro, G., Characters and blocks of finite groups, London Mathematical Society Lecture Note Series, 250. Cambridge University Press, Cambridge, 1998.

Alperin, J. L., Local representation theory, Cambridge Studies in Advanced Mathematics, 11. Cambridge University Press, Cambridge, 1986.

Curtis, C. W. and Reiner, I., Methods of representation theory, vol. I/II, Pure and Applied Mathematics, John Wiley & Sons, Inc., New York, 1981/1987.

Schedule:

Apr 02: Initial meeting
Apr 11: Chap. 1&2 (Background/Basics), Exercises 1.7, 1.8, 1.9, 1.13(a), 1.15; 2.1, 2.2, 2.7, 2.8, 2.9, 2.10 [Jonas]
Apr 18: Chap. 3 (Characters), Exercises 3.4, 3.8, 3.11, 3.12, 3.14, 3.15 [Tobias]
Apr 25, 10:30: Chap. 4 (Construction of Modules/Characters) [Jonas]
May 02: Chap. 5 (Mackey/Clifford) and Exercises from Chapters 4&5, e.g., 4.4, 4.6, 4.7, 4.11, 4.17; 5.1, 5.2, 5.7, 5.8, 5.10 [Tom]
May 08, 14:30: Chap. 6 (p-groups and the Radical, without Jennings) [Jonas]
May 16: Chap. 7 (Projective Modules for Algebras), Exercises 7.1-7.6, 7.8, 7.9, 7.11 [Jonas]
May 23: Chap. 8 (Projective Modules for Group Algebras, 8.2.1 up until 8.4.1 may be skipped) [Tobias/Jonas]
May 29, 14:30: Sections 9.1-9.3 of Chap. 9 (Splitting fields) and Appendix A (Discrete valuation rings) [Jonas/Tobias]
Jun 06: Remainder of Chap. 9 (i.e. 9.4 - 9.6: Reduction mod p & Decomposition map; cde triangle; Blocks of defect 0) [Tom]
Jun 12, 14:30: Chap. 10 (Brauer characters), Exercises 10.1, 10.2 [Jonas]
Jun 20: Sections 11.1-11.4 of Chap. 11 (Krull-Schmidt; relative projectivity; finite representation type) [Jonas/Tobias]
Jun 27: Remainder of Chap. 11 (Vertices/Sources/Green correspondence; Heller operator) [Tom]
Jul 03: Sections 12.1-12.4 of Chap. 12 (Blocks of rings/groups and the defect group) [Jonas/Tobias]
Jul 04: Brauer trees and computing Brauer characters [Klaus]
Jul 18: Remainder of Section 12 [Jonas]