AIS - Representation Theory of Quivers and BGG Category O for semi simple Lie Algebras (2024)
Speakers and Syllabus
Syllabus:
|
Name of the Speaker with affiliation |
No. of Lectures + |
Detailed Syllabus |
|
|
Shraddha Srivastava Dept. of Maths. IIT Dharwad |
4.5+3 |
Lie algebras (definition and notation etc), classical Lie algebras, Semisimple Lie algebras, Weyl’s theorem, Representations of sl(2, C). |
|
|
Sachin Sharma Dept. of Maths and Stats IIT Kanpur |
4.5+3
|
Root systems, Weyl groups, Dynkin diagrams: classification of irreducible root systems. |
|
|
Upendra Kulkarni Dept. of Maths. CMI, Chennai |
9+6 |
Representations of quivers, Projective and injective representations, Dynkin diagrams and Gabriel’s theorem |
|
|
R. Venkatesh Dept. of Maths. IISc, Bangalore |
4.5+3 |
Universal enveloping algebras, PBW theorem, Serre’s theorem. |
|
|
B. Ravinder Dept. of Maths and Stats IIT Tirupati |
4.5+3 |
Representation theory of semisimple Lie algebras, highest weight modules, Verma modules, classification of finite dimensional modules. Characters, Harish-Chandra theorem
|
|
|
Amit Kuber Dept. of Maths and Stats. IIT Kanpur |
9+6 |
Path algebras and bound quiver algebras, Auslander-Reiten Theory: Almost split sequences, Auslander-Reiten quiver, Auslannder-Reiten formulas |
|
|
Apoorva Khare Dept. of Maths. IISc, Bangalore |
9+6 |
Basic properties of Category O, projective covers of simple highest weight modules, splitting into blocks, Verma/standard flags of projective modules, endomorphism algebra of projective generator, BGG reciprocity. |
|
|
Thomas Brüstle Dept of Maths Sherbrook University Canada |
9+6 |
Recent trends in quiver representations Part 1: Cluster algebras and quiver representations Part 2: Gentle algebras and geometric models |
|
References:
- Schiffler, Ralf. Quiver representations. (2014) CMS Books in Mathematics, Springer.
- Auslander, M., Reiten, I., & Smalo, S. (1995). Representation Theory of Artin Algebras (Cambridge Studies in Advanced Mathematics). Cambridge: Cambridge University Press.
- Assem, I., Skowronski, A., & Simson, D. (2006). Elements of the Representation Theory of Associative Algebras: Techniques of Representation Theory (London Mathematical Society Student Texts). Cambridge: Cambridge University Press.
- Crawley-Boevey W., Lectures on representations of quivers. Available at https://www.math.uni-bielefeld.de/~wcrawley/quivlecs.pdf
- Bernhard Keller, Cluster algebras, quiver representations and triangulated categories, arXiv:0807.1960 (sections 1-6)
- Bernhard Keller, Cluster algebras and derived categories, arXiv:1202.4161 (sections 1-5).
- Sebastian Opper, Pierre-Guy Plamondon, and Sibylle Schroll, A geometric model for the derived category of gentle algebras, arXiv:1801.09659.
- Humphreys, J. E. (2012). Introduction to Lie algebras and representation theory (Vol. 9). Springer Science \& Business Media.
- Humphreys, J. E. (2008). Representations of Semisimple Lie Algebras in the BGG Category O (Vol. 94). American Mathematical Soc.
- Bernstein, I. N. and Gel'fand, I. M. and Gel'fand, S. I. (1976). Category of g-modules. Functional analysis and its applications, 10(2), 87—92.
List of Tutors
|
Tutor
|
Affiliation
|
|
Dr. G.V. Krishna Teja
|
ISI Bengaluru
|
|
Ritesh Pandey
|
IIT Kanpur
|
|
Esha Gupta
|
Université Paris-Saclay
|
|
Subham Jaiswal
|
ISI Kolkata
|
|
Riju Bindua
|
IIT Delhi
|
Time Table
|
Day |
Date |
Lecture 1 |
Tutorial 1 |
Lecture 2 |
Tutorial 2 |
|
Week 1 |
Inauguration at 9:20 by Prof. K.N. Raghavan |
(9.30–11.00) |
(11.30-12.30) |
(2.00-3:30) |
(4.00-5.00) |
|
Mon |
02/12/24 |
SSr |
SSr+RP |
UK |
UK+SJ |
|
Tues |
03/12/24 |
SSr |
SSr+RP |
UK |
UK+SJ |
|
Wed |
04/12/24 |
SSr |
SSr+RP |
UK |
UK+SJ |
|
Thu |
05/12/24 |
SSh |
SSh+RP |
UK |
UK+SJ |
|
Fri |
06/12/24 |
SSh |
SSh+RP |
UK |
UK+SJ |
|
Sat |
07/12/24 |
SSh |
SSh+RP |
UK |
UK+SJ |
|
Week 2 |
|
(9.30–11.00) |
(11.30-12.30) |
(2.00-3:30) |
(4.00-5.00) |
|
Mon |
09/12/24 |
RV |
RV |
AKu |
AKu+EG |
|
Tues |
10/12/24 |
RV |
RV |
AKu |
AKu+EG |
|
Wed |
11/12/24 |
RV |
RV |
AKu |
AKu+EG |
|
Thu |
12/12/24 |
BR |
BR |
AKu |
AKu+EG |
|
Fri |
13/12/24 |
BR |
BR |
AKu |
AKu+EG |
|
Sat |
14/12/24 |
BR |
BR |
AKu |
AKu+EG |
|
Week 3 |
|
(11:00-12:30) |
(12:45-1:45) |
(2:45-4:15) |
(4:30-5:30) |
|
Mon |
16/12/24 |
AKh |
AKh+GKT |
TB |
TB+EG+RB |
|
Tues |
17/12/24 |
AKh |
AKh+GKT |
TB |
TB+EG+RB |
|
Wed |
18/12/24 |
AKh |
AKh+GKT |
TB |
TB+EG+RB |
|
Thu |
19/12/24 |
AKh |
AKh+GKT |
TB |
TB+EG+RB |
|
Fri |
20/12/24 |
AKh |
AKh+GKT |
TB |
TB+EG+RB |
|
Sat |
21/12/24 |
AKh |
AKh+GKT | TB | TB+EG+RB |
UK: Upendra Kulkarni, SSr: Shraddha Srivastava, SSh: Sachin Sharma, AKu: Amit Kuber, RV: R. Venkatesh, BR: B. Ravinder, TB: Thomas Brüstle, AKh: Apoorva Khare, RP: Ritesh Pandey, SJ: Subham Jaiswal, EG: Esha Gupta, GKT: G. Krishna Teja, RB: Riju Bindua