Main Reference: [BZ76] I. N. Bernstein and A. V. Zelevinsky,
Representation theory of GL(n, F), where F is a non-Archimedean local field,
Russian Mathematical Surveys, 31 (1976), no. 3, 1–68.
Other Reference: [BZ77] I. N. Bernstein and A. V. Zelevinsky,
Induced representations of reductive p-adic groups. I,
Annales Scientifiques de l'École Normale Supérieure,
(4) 10 (1977), no. 4, 441–472.
Meeting time: Mondays 10:00 AM
| Time | Contents | Speaker | Remarks |
|---|---|---|---|
| Oct.22 | Distributions on l-spaces, l-groups | Yuichi | P1-13 |
| Oct.29 | Representations of l-groups | Jimmy | P10-16 |
| Nov.05 | l-sheaves | Yuzheng | P10 |
| Nov.12 | Representations of l-groups, Modules, πN, Schur’s Lemma | Kewen | P19 |
| Nov.19 | The Contragradient representation, tensor product of reps | Yuichi | P20 |
| Nov.26 | Character, induced rep, Frobenius Reciprocity, Jacquet Functor | Alan | P24 |
| Dec.03 | Finite (compact) representations | Kewen | P28 |
| Jan.21 | Induced and quasi-cuspidal representations | Kewen | Till 3.11 |
| Jan.28 | Partitions, general theory | Kewen | Section 3 |
| Feb.11 | Functors, Jacquet's theorem | Kewen | Section 3 |
| Feb.17 | Cuspidal representations | Jimmy | Section 4 |
| Mar.24 | The Gelfand-Kazhdan theory | Alan | Chapter 3 |
| Apr.07 | Proofs of Section 5 | Kewen | Chapter 3 |
Starting from here, we turned to read some automorphic representation references as well as the local ones:
Main Reference: [Ge75] S. Gelbart,
Automorphic Forms on Adele Groups,
Princeton University Press, 1975.
Other Reference: [Bu97] D. Bump,
Automorphic Forms and Representations,
Cambridge Studies in Advanced Mathematics, vol. 55,
Cambridge University Press, 1997.
Meeting time: Mondays 12:01 PM EST
| Time | Content | Speaker | Chapter (of [Ge75]) |
|---|---|---|---|
| Apr.14 | The Classical Theory | Ziqian | Chapter 1 |
| Apr.21 | Automorphic Forms and Decomposition of L2(Γ\SL(2,R)) | Alan | Chapter 2 |
| Apr.28 | Automorphic Forms on Adele group of GL(2) | Haoran.L, Yuzheng | Chapter 3 |
| May.05 | Representations of GL(2), local and global | Yu | Chapter 4 |
| May.12 | Cusp Forms and Representations of GL(2) | Yuzheng | Chapter 5 |
| May.19 | Hecke Theory for GL(2) | Haoran.L, Xinran | Chapter 6 |
| May.26 | Construction of Some Automorphic Forms | Xinran | Chapter 7 |
| Jun.02 | Eisenstein Series and the Continuous Spectrum | Alan | Chapter 8 |
| Jun.09 | Trace Formula for GL(2) | Chapter 9 | |
| Jun.16 | Automorphic Forms on Quaternion Algebra | Haoran.L | Chapter 10 |
* Rows in bold are expected to be covered in more than one meeting.
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