NCMW - Representations of p-adic groups (2022)
Speakers and Syllabus
Syllabus to be covered in terms of modules of 6 lectures each :
Name of the Speakers with their affiliation. |
No. of Lectures |
Detailed Syllabus |
CG Venketasubramanian | Bernstein-Zelevinsky theory including combinatorial classification of irreducible admissible representations of p-adic general linear groups in terms of supercuspidal representations and multisegments, the work of Lapid and Minguez on ladder representations. | |
Tanmay Deshpande | Realization of various supercuspidal representations of p-adic reductive groups in the cohomology of affine Deligne-Lusztig varieties. |
|
Manish Mishra | Compact induction, J.-K. Yu’s construction of supercuspidal repre- sentations, Bushnell-Kutzko theory of types and covers. |
|
Santosh Nadimpalli | Construction and analysis of representations of finite groups of Lie type, Deligne-Lusztig theory. |
|
Ravi Raghunathan | Modular and automorphic forms, connection between global and local representation theory, L-functions and their integral representations. |
|
Sandeep Varma | The Bruhat-Tits building, parahohoric groups, Moy-Prasad filtrations. |
References:
- Bump, Daniel Automorphic forms and representations. Cambridge Studies in Advanced Mathematics, 55. Cambridge University Press, Cambridge, 1997. xiv+574 pp.
- Bushnell, Colin J.; Kutzko, Philip C. The admissible dual of GL(N) via compact open subgroups. Annals of Mathematics Studies, 129. Princeton University Press, Princeton, NJ, 1993. xii+313 pp.
- Ottawa lectures on admissible representations of reductive p-adic groups. Lectures from the Field Institute Workshops held at the University of Ottawa, Ottawa, ON, May 2004 and January 2007. Edited by Cli↵ton Cunningham and Monica Nevins. Fields Institute Monographs, 26. American Mathematical Society.
- Digne, Francois; Michel, Jean. Representations of Finite Groups of Lie Type. Cam-bridge University Press.
References (Research articles).
- Bernstein, I. N. and Zelevinsky, A.V. Representations of the group GL(n, F), where F is a local non-Archimedean field. Uspehi Mat. Nauk 31 (1976). Available at: http://www.math.tau.ac.il/⇠bernstei/Publication list/Publication list.html
- Bruhat, F; Tits, J. Groupes rductifs sur un corps local. Inst. Hautes Etudes Sci. ́ Publ. Math. No. 41 (1972), 5-251-.
- Bruhat, F; Tits, J. Groupes rductifs sur un corps local. II Sch ́emas en groupes.Existence d’une donn ́ee radicielle valu ́ee. Inst. Hautes Etudes Sci. Publ. Math. ́ No. 60 (1984), 197-376.
- Lapid, Erez; Mnguez, Alberto On a determinantal formula of Tadi ́c. Amer. J. Math 136 (2014), no. 1, 111-142.
- Moy, Allen; Prasad, Gopal. Unrefined minimal K-types for p-adic groups. Invent. Math. 116 (1994), no. 1-3, 393-408.
- Bushnell, Colin J.; Kutzko, Philip C. Smooth representations of reductive p-adic groups: structure theory via types. Proc. London Math. Soc. (3) 77 (1998), no. 3, 582-634.
- Jacquet, H.; Piatetskii-Shapiro, I. I.; Shalika, J. A. Rankin-Selberg convolutions. Amer. J. Math. 105 (1983), no. 2, 367-464.
- Gelbart, Stephen S. Automorphic forms on adle groups. Annals of Mathematics Studies, No. 83. Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975. x+267 pp.
Tentative Schedule
- Course 1 - Representations of Finite Groups of Lie Type: by Santosh Nadimpalli (SN).
- Course 2 - Representations of General Linear Groups over p-adic Fields: by CG Venketasubramanian (CGV).
- Introductory lectures; and Course 3 - Bruhat-Tits theory: by Sandeep Varma (SV).
- Course 4 - Types and Construction of Supercuspidal Representations: by Manish Mishra (MM).
- Course 5 - Realizing representations of p-adic groups using affine Deligne-Lusztig varieties: by Tanmay Deshpande (TD).
- Course 6 - Automorphic Representations and L-functions (by RR).
Time Table
Week 1
Day | Date | 9:30-10:45 | 11:15-12:30 | 14:15-15:30 | 16:00-17:00 (Tutorial) |
M | May 23 | SV (Introductory) |
SN | SV (Introductory) |
Tutorial (Course 1) |
T | May 24 | SN | CGV | SV | Tutorial (Course 2) |
W | May 25 | SN | CGV | SV | Tutorial (Course 3) |
Th | May 26 | SN | CGV | SV | Tutorial (Course 1) |
F | May 27 | SN | CGV | SV | Tutorial (Course 2) |
S | May 28 | SN | CGV | SV | Tutorial (Course 3) |
Week 2
Day | Date | 9:30-10:45 | 11:15-12:30 | 14:15-15:30 | 16:00-17:00 (Tutorial) |
M | May 30 | MM | TD | RR | Tutorial (Course 4) |
T | May 31 | MM | TD | RR | Tutorial (Course 5) |
W | June 1 | MM | RR | TD | Tutorial (Course 6) |
Th | June 2 | MM | TD | RR | Tutorial (Course 4) |
F | June 3 | MM | TD | RR | Tutorial (Course 5) |
S | June 4 | MM | RR | TD | Tutorial (Course 6) |
10:45 - 11:15 and 15:30 - 16:00 will be tea breaks, while 12:30 - 14:15 will be a lunch break.