This is the home page for the 2020 LTCC course on Representations of p-adic groups.

Some notes and exercises for the first week are here. I've edited this to match what I covered. For a brief introduction to the p-adic numbers I think Chapter II in Serre's "A Course in Arithmetic" is good.

Some notes and exercises for the second week are here.

Some notes and exercises for the third week are here.

Some notes and exercises for the fourth week are here.

Notes for the fifth and final week are here. I will not be giving the lecture, apologies! Happy to answer questions over email or arrange a virtual meeting.

• Savin, notes on Representations of p-adic Groups www.ims.nus.edu.sg/Programs/liegroups/files/sing.pdf
• Prasad and Raghuram, Representation theory of GL(n) over non-Archimedean local fields www.math.tifr.res.in/~dprasad/ictp2.pdf
• Bernstein and Zelevinsky, Representations of the group GL(n,F) www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/B-Zel-RepsGL-Usp.pdf A survey paper with detailed proofs. The notation is a little non-standard.
• Casselman, Introduction to the theory of admissible representations of p-adic reductive groups www.math.ubc.ca/~cass/research/pdf/p-adic-book.pdf