Advanced Instructional School (AIS)- Representation Theory

Venue: Pune Univ. & BIM
Dates: 2 - 28 July, 2007


Convener(s) Speakers, Syllabus and Time table Applicants/Participants


School Convener(s)

Name Dipendra Prasad A. K. Bhandari S. A. Katre (Local Co-ordinator)
Mailing Address

TIFR, Mumbai

Panjab University, Chandigarh

University of Pune

Advanced Instructional School on Representation Theory and its Applications (AIS-RTA) is being organised in Pune in July 2007 on behalf of NBHM.

 National Coordinating Committee
Director: Ravi S. Kulkarni
Secretary: J. K. Verma
Members : S. D. Adhikari, Satya Deo, S. A. Katre, Shobha Madan, I. B. S. Passi, Ravi A. Rao

Members of the Local Organising Committee

Bhaskaracharya Pratishthana: C. S. Inamdar (Custodian), R. V. Gurjar (Res. Director, Hon.), R. R. Simha
University of Pune: B .N. Waphare (HOD, Maths.), S. A. Katre, H. Bhate

Speakers and Syllabus 

  • Representation theory of groups is one of the most beautiful subjects in mathematics which finds applications to many other subjects including Physics and Chemistry, besides being of fundamental importance to numerous areas of mathematics. The aim of this summer school will be to offer a first course in representation theory of finite as well as compact groups. After developing the general theory, the school will try to emphasize representation theory of specific groups such as SU(2), SL(2,F_q), and the symmetric groups, which forms building blocks for representation theory of more complicated groups. There will be some lectures on applications of representation theory to Number theory, as well as combinatorics, and perhaps an example from the work of the Fields medalist Okounkov's work. There will be some lectures too to bring out the historical perspective of the subject.

  Proposed Syllabus and Speakers

1. Ashwani Bhandari: Basic Review of group theory with notions about the group acting on sets, the class equation, some uses, such as Sylow's theorem quickly done, conjugacy classes, symmetric group, the structure of their conjugacy classes, semi-simple rings and modules, Wedderburn structure theorem, application to the structure of group ring, and to representation theory of the group.
2.S. V. Kanetkar: Representation theory of finite groups with basic theorems proved without recourse to Wedderburn theory. Character table, Induced representations, Mackey irreducibility theorem, Clifford theory. Examples.
3. Maneesh Thakur: Representation theory of the symmetric group in terms of the Young tableau. The Schur-Weyl duality between GL(n) and S_m.
4. Ravi Kulkarni: Introduction to representation theory of compact Lie groups, with special emphasis on SU(2).
5. Amritanshu Prasad: Representation theory of GL(2,F_q), SL(2,F_q). Beginning of the story for GL(n,F_q) with parabolic induction, and irreducibility of it.
6. M .K. Srinivasan: Combinatorial applications of representation theory.

1. J-P. Serre, Linear Representations of Finite Groups.
2. C. Musili, Representations Finite Groups, Hindustan Book Agency, 1993.
3. W. Fulton, J. Harris, Representation Theory: A first course, Graduate Texts in Mathematics.
   Readings in Mathematics 129. Springer Verlag (1991). International Edition (Low priced Ed.)
4. B. Simon: Representations of Finite and Compact Groups, Graduate Studies in Mathematics, vol. 10, AMS (1997).
5. E. B. Vinberg: Linear Representations of Groups, Birkhäuser (1988).

UM Lectures

1. I.B.S. PASSI : Historical Overview of Representation Theory

2. R. SRIDHARAN : Meromorphicity of Artin L functions

Note: All the participants will be given the book ``Representation Theory, A First Course", by W. Fulton, J. Harris (Springer).

Associate Teachers
1. Uma Ayer email: uma.iyer at
2. Anupam Kumar Singh email: anupam at
3. Pooja Singla e-mail: pooja at

Time table

  2nd, Mon. 3rd, Tue. 4th, Wed. 5th, Thur, 6th, Fri 7th, Sat
     9.30 - 11.00  AKB AKB AKB AKB AKB AKB
     11.00 - 11.30  Tea
     11.30 - 1.00  SVK SVK SVK SVK SVK SVK
     1.00 - 2.15  Lunch
     2.15 - 3.15  AKB-Tut SVK-Tut AKB-Tut SVK-Tut AKB-Tut AKB-Tut
     3.15 - 3.45  Library / Tea
     3.45 - 5.15  SVK-Tut AKB SVK-Tut AKB SVK-Tut ---


  9th, Mon 10th,Tue 11th, Wed 12th, Thurs 13th, Fri 14th, Sat
     9.30 - 11.00  MT MT MT MT MT MT
     11.00 - 11.30  Tea
     11.30 - 1.00  SVK SVK RK RK RK RK
     1.00 - 2.15  Lunch
     2.15 - 3.15  MT-Tut SVK-Tut MT-Tut MT-Tut MT-Tut ---
     3.15 - 3.45  Library / Tea ---
     3.45 - 5.15  DT DT Sem/Tut RK-Tut RK-Tut --


  16th, Mon 17th, Tue 18th, Wed 19th, Thur 20th, Fri 21st, Sat
     9.30 - 11.00  AP AP AP AP AP AP
     11.00 - 11.30  Tea
     11.30 - 1.00  RK RK RK RK MS MS
     1.00 - 2.15  Lunch
     2.15 - 3.15  AP-Tut AP-Tut AP-Tut AP-Tut AP-Tut Math Video
     3.15 - 3.45  Library / Tea
     3.45 - 5.15  RK-Tut RK-Tut RK-Tut RK-Tut MS-Tut Cultural Evening


  23rd, Mon. 24th, Tue. 25th, Wed. 26th, Thur 27th, Fri. 28th, Sat
9.30 - 11.00  MS MS MS MS MS MS
11.00 - 11.30  Tea
11.30 - 1.00  AP AP RS RS RS RS
1.00 - 2.15 Lunch
2.15 - 3.15 MS-Tut MS-Tut MS-Tut MS-Tut MS-Tut FeedBack Session
3.15 - 3.45  Library / Tea Valedictory Function
3.45 - 5.15 AP-Tut IBSP IBSP IBSP IBSP ---


  AKB-Ashwani K. Bhandari SVK- S.V. Kanetkar RK- Ravi Kulkarni,
  MT-Maneesh Thakur AP-Amritanshu Prasad MS-Murali Srinivasan
UM-Lecture Series: IBSP- I.B.S.Passi RS- R.Sridharan DT- Dinesh Thakur

Lecture notes and problems at AIS-RTA, 2007
Prof. A. K. Bhandari      
Dr. S. V. Kanetkar
Prof. Amritanshu Prasad     visit here for updated version of his notes
Prof. Maneesh Thakur
Prof. Ravi Kulkarni      
Prof. Murali Srinivasan
Exercises collected by Prof. A. Raghuram

Click here to download problems and notes

Selected Applicants


Sr. No. Name Place Accommodation: H-Rooms at Guest House of BP, R-Rooms at main building of BP, Flat-is flat near BP,
P.U.-Univ. Pune
1. Lokesh Kumar Joshi G.B.Pant Univ. of Agric. & Tech. Pantanagar, U.P. P.U.
2. Ms. Viji M. Cochin University of Science and Technology, Cochin R-1
3. Ms. Tanusree Pal HRI, Allahabad, UP R-1
4. Sudarshan Gurjar TIFR, Mumbai R-5
5. Ms. V. Divya ISI, Bangalore. R-1
6. Wajih Ashraf A. M. Univ., Aligarh, U.P. H-3
7. Niraj Prasad Mumbai University, Mumbai, Maha. Flat
8. Akhlad Iqbal A. M. University, Aligarh, U.P. H-3
9. Fahad Sikander A. M. University, Aligarh, U.P. H-3
10. Ziaul Hoque A. M. University, Aligarh, U.P. H-2
11. Muzibur Rahman Mozumder A. M. University, Aligarh, U.P. H-2
12. Dr. Atul Razdan University of Delhi, Delhi H-2
13. Ms. Preena Samual I.M.Sc., Chennai R-2
14. Aftab Hussain Shah A. M. University, Aligarh, U.P. H-3
15. Somnath Jha TIFR, Mumbai R-5
16. Anuj Kumar G.B.Pant Univ. of Agric. & Tech. Pantanagar, U.P. P.U.
17. Mohd Tanveer A. M. University, Aligarh, U.P. H-2
18. Dinesh Bisht G.B.Pant Univ. of Agric. & Tech. Pantanagar, U.P. P.U.
19. Alpesh Kumar Dhorajia I.I.T. Bombay Powai, Mumbai, Maha. Flat
20. Surinder Pal Singh Kainth I.I.T. Bombay Powai, Mumbai, Maha. Flat
21. T. Sakthivel Periyar University, salem-ll, Tamilnadu Flat
22. Ms. Manasi Mahapatra Inst. of Maths & Applications, Bhubaneswar, Orissa R-2
23. Prasenjit Bhowmik IIT, Guwahati, Assam R-5
24. Ramesh R. Periyar University, salem-ll, Tamilnadu Flat
25. S. Petchimuthu Periyar University, salem-ll, Tamilnadu Flat
26. Shiv Narain Kurukshetra University, Kurukshetra Flat
27. Shane D'Mello TIFR, Mumbai R-5
28. Ms. Mousumi Mandal I.I.T. Bombay Powai, Mumbai, Maha. R-2
29. Shivaji Tarate New Arts, Comm. & Science College, A'Nagar, Maha. P.U.
30. Phatangare Nanasaheb M. New Arts, Comm. Sci. College, Ahmednagar, Maha. flat
31. Sharad Hegde Karnatak University, Dharwad, Karnatak P.U.
32. Dr. H. Pattanayak Reveshaw Univ., Cuttak, Orissa. flat
33. Rajib Haloi Tezpur Univ., Napaam, Sonitpur, Assam R-5
34. Pawan Kumar IIT, Guwahati, Assam R-5
35. Samrith Ram IIT-Bombay, Powai, Mumbai, Maha. Flat
36. Ashay Burungale ISI, Bangalore R-5

List of Local Participants

37. Jagmohan Tanti Bhaskaracharya Pratishthana (BIM), Pune, Maha.
38. Devendra Shirolkar Dept. of Maths, Univ. of Pune, Pune, Maha.
39. Ms. Kavita Sutar NorthEastern University, Boston
40. Rajanish Malekar N.D.A., Pune
41. Ms. Manjusha S. Joshi Bhaskaracharya Pratishthana and Maybole Technologies, Pune
42. Ashwin Deopurkar Chennai Mathematical Institute, Chennai


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