AIS - Schur Multiplier and Representation Theory (2025)
Speakers and Syllabus
Detailed syllabus
|
Speaker |
No. of Lectures (90 min.) |
Detailed Syllabus |
|
Sunil K Prajapati (IIT Bhubaneswar) |
2 |
Group Representation (GR): Group representations and characters, Maschke’s Theorem and Complete Reducibility, Orthogonality Relations |
|
Amit Kulshrestha (IISER Mohali) |
2 |
Irreducibility Criteria (IC): Frobenius reciprocity theorem, conjugate representation, Mackey Irreducibility criteria, Wigner-Mackey Method of Little Group |
|
Shripad Garge (IIT Bombay) |
6 |
Group Cohomology (GC): Cohomology Groups, Second cohomology group, and central extensions, The homomorphism restriction, inflation and transgression, Hochschild-Serre exact sequence |
|
Sumana Hatui (NISER Bhubaneswar) |
4 |
Projective Representation (PR): Projective representation, twisted group algebra, representation groups (existence and characterization) |
|
Pradeep Rai (Mahindra University, Hyderabad) |
6 |
Schur Multiplier (SM): Basic results, Schur Multiplier of abelian groups, Schur’s formula, covering groups, exponent and central quotient, some results on p-groups |
|
Anupam Kumar Singh (IISER Pune) |
4 |
General linear group over F_q (GLG): Representations of GL_2(F_q) |
References:
- M. Isaacs, Character Theory of Finite Groups
- C. W. Curtis, Pioneers of Representation Theory
- J. Alperin and R. Bell, Groups and Representations
- G. Karpilovsky, Projective Representations of Finite Groups
- G. Karpilovsky, The Schur Multiplier
- J.-P. Serre, Linear Representations of Finite Groups
- W. Fulton and J. Harris, Representation Theory
- D.J. Benson, Representations and Cohomology, Volumes I and II
Tutor's Name with affiliation:
- Ram Karan Choudhary, IIT Bhubaneswar
- Saikat Panja, ISI Bangalore
- Vipul Kakkar, Central University of Rajasthan, Ajmer
- Harish Krishnani, IISER Mohali
Time Table
|
Day |
Date (Dec 2025) |
Lecture 1 (9:30-11) |
Tea (11:05-11:25) |
Lecture 2 (11:30-1:00) |
Lunch (1:05-2:25) |
Tutorial Session (TS) (2:30-3:30) |
Tea (3:35-3:55) |
Tutorial Session (TS) (4:00-5:00) |
Snacks (5:05-5:30) |
|
Thur |
04 |
SKP |
|
SG |
|
TS- GC |
|
TS- GC |
|
|
Fri |
05 |
SKP |
SG |
TS- GR |
TS- GR |
||||
|
Sat |
06 |
AK |
SG |
TS- GC |
TS- GC |
||||
|
Sun |
07 |
AK |
SG |
TS- IC |
TS- IC |
||||
|
Mon |
08 |
SH |
SG |
TS- GC |
TS- GC |
||||
|
Tues |
09 |
SH |
SG |
TS- PR |
TS- PR |
||||
|
WEDNESDAY-OFF |
|||||||||
|
Thur |
11 |
PKR |
|
SH |
|
TS- PR |
|
TS- PR |
|
|
Fri |
12 |
PKR |
SH |
TS- SM |
TS- SM |
||||
|
Sat |
13 |
PKR |
AKS |
TS- PR |
TS- GLG |
||||
|
Sun |
14 |
PKR |
AKS |
TS- SM |
TS- SM |
||||
|
Mon |
15 |
PKR |
AKS |
TS- GLG |
TS- GLG |
||||
|
Tues |
16 |
PKR |
AKS |
TS- SM |
TS- SM |
||||
Full forms for the abbreviations of speakers:
SKP: Sunil Kumar Prajapati (IIT Bhubaneswar)
AK: Amit Kulshrestha(IISER Mohali)
SG: Shripad Garge (IIT Bombay)
SH: Sumna Hatui (NISER Bhubaneswar)
PKR: Pradeep Kumar Rai (Mahindra University)
AKS: Anupam Kumar Singh (IISER Pune)
Full forms for the abbreviations related to the Tutorial session and Tutors' Name:
-
TS- GR and TS- IC:Tutorial session on Group Representation (GR) and Irreducibility Criteria (IC)- Ram Karan Choudhary (IIT Bhubaneswar)
-
TS- GC and TS- GLG: Tutorial session on Group Cohomology (GC) and General linear group over F_q (GLG)- Saikat Panja (ISI Bangalore)
-
TS- PR: Tutorial session on Projective Representation (PR)- Harish Krishnani (IISER Mohali)
-
TS- SM: Tutorial session on Schur Multiplier (SM)- Vipul Kakkar (Central University of Rajasthan, Ajmer)