Combinatorial models in Representation Theory (2019)

Convener(s)

 
Name: K N Raghavan S Viswanath
Mailing Address:

The Institute of Mathematical Sciences
IV Cross Road, CIT Campus
Taramani
Chennai 600 113
Tamil Nadu, India.

 The Institute of Mathematical Sciences
IV Cross Road, CIT Campus
Taramani
Chennai 600 113
Tamil Nadu, India.
Email:  knr.imsc at gmail.com  svis at imsc.res.in

Please Note:  Participants have to arrange for their own travel.

Dates: 

Monday, November 4, 2019 - 09:30 to Saturday, November 16, 2019 - 18:15

Venue: 

Venue Address: 

The Institute of Mathematical Sciences
IV Cross Road, CIT Campus
Taramani
Chennai 600 113
Tamil Nadu, India.

Venue State: 

Venue City: 

PIN: 

600113

Chrono Order: 

335

Syllabus: 

  • Module A (B Ravinder, CMI) Young tableaux and the representation theory of the Lie algebra sln C: Review of some aspects of the general theory of representations of complex semisimple Lie algebras, the special case of sln C, highest weights and partitions, irreducible characters in terms of semistandard Young tableaux, Gelfand-Tsetlin patterns, Schur functions, the dimension formula, decomposing tensor products, the Littlewood- Richardson rule, Demazure modules.
  • Module B (Amritanshu Prasad, IMSc) The plactic monoid: Words, Knuth equivalence, plactic and coplactic classes, crystal operators on words, the Robinson-Schensted correspondence, Schur-Weyl duality.
  • Module C (KN Raghavan and S Viswanath, IMSc) The Littelmann path model: Paths, root operators, Lakshmibai-Seshadri paths, the character formula, tensor product decomposition in terms of paths, the Weyl group action, the crystal isomorphism theorem.
  • Module D (R Venkatesh, IISc) Affine Lie algebras and their representations: Affine Lie algebras as central extension of loop algebras, highest weight representations, Weyl-Kac character formula, character of the basic representation.
  • Module E (S Viswanath, IMSc) Affine crystals: An overview of various combinatorial models of crystals for the affine Lie algebra sln , such as partitions, LS paths, abacus, semi-infinite paths etc.
  • Module F (KN Raghavan, IMSc) Constructing nice bases for representations from path data: Using paths or other crystal models to construct bases with nice properties, such as compatibility with Demazure modules. Standard monomial theory, geometric applications.

Speakers

  1. B Ravinder (BR), CMI
  2. Amritanshu Prasad (AP), IMSc
  3. K N Raghavan (KNR), IMSc
  4. S Viswanath (SV), IMSc
  5. R Venkatesh (RV), IISc

Link to site

Time Table: 

Tea Breaks: 11.00 - 11.30 and 3.30 - 4.00
Lunch Break: 1.00 - 2.00
Snacks: 5.00 - 5.30

  9.30 - 11.00
Lecture 1		 11.30-1.00
Lecture 2		 2.00-3.30
Lecture 3		 4.00-5.00
Tutorial
Nov 04 BR AP KNR BR, AP, KNR
Nov 05 BR AP KNR BR, AP, KNR
Nov 06 BR AP KNR BR, AP, KNR
Nov 07 BR AP SV BR, AP, SV
Nov 08 BR AP SV BR, AP, SV
Nov 09 BR AP SV BR, AP, SV
Nov 11 RV SV KNR RV, SV, KNR
Nov 12 RV SV KNR RV, SV, KNR
Nov 13 RV SV KNR RV, SV, KNR
Nov 14 RV SV KNR RV, SV, KNR
Nov 15 RV SV KNR RV, SV, KNR
Nov 16 RV SV KNR RV, SV, KNR

Selected Applicants: 

 

Sr.n SID Full Name Gender Affiliation Position in College/ University University/Institute M.Sc./ M.A. Year of Passing M.Sc./ M.A Ph.D. Degree Date
1 27574 Mr. Niranjan Nehra Male IISER Mohali PhD IIT Kanpur 2017  
2 27575 Ms. Shushma Rani Female IISER Mohali PhD Punjabi University Patiala 2015  
3 28433 Mr. Promod Sharma Male IIT(BHU) Research Scholar Assam University Silchar 2017  
4 28504 Mr. Souvik Pal Male Harish-Chandra Research Institute PhD IMSc 2016  
5 28983 Mr Krishna Teja Gv Male Indian Institute of Science Bangalore 4th year Ph.D student Central University of Tamil Nadu 2016  
6 29013 Mr. Ayush Udeep Male IIT Bhubaneswar PhD Central University of South Bihar 2016  
7 29049 Dr. V. Ramanathan Male Periyar University Postdoctoral Fellow G. Venkataswamy Naidu College, Kovilpatti. 2010 27/10/2017
8 29137 Mr. Krishanu Roy Male The Institute of Mathematical Sciences SRF      
9 29166 Mr. Sundaresan P Male Pondicherry University PhD Pondicherry University 2017  
10 29228 Dr. Sudip Bera Male Indian Institute of Science, Post-Doc M.Sc-Calautta University 2012 16/06/2019
11 29296 Mr. Joyentanuj Das Male IISER Trivandrum PhD Student IISER TVM 2018  
12 29319 Ms. Amrutha P Female IISER-TVM Ph.D. Student IISER-TVM 2017  
13 29322 Dr. Bikramaditya Sahu Male Indian Institute of Science Post-Doctoral Fellow IIT Bombay 2013 24/12/2018
14 29478 Mr Priyanshu Chakraborty Male Harish chandra research institute phd universityof calcuta 2017  
15 29529 Ms Shraddha Srivastava Female The Institute of Mathematical Sciences Post-doctoral felllow IIT Bombay 2011 29/08/2017
16 29640 Mr. Subhajit Ghosh Male Indian Institute of Science Int. Ph.D. Indian Institute of Science, Bangalore 2015  
17 29674 Mr. G. Arunkumar Male Indian Institute of Science Education and Research, Mohali. Postdoctoral fellow. Ayyanadar Janakiammal College, Sivakasi. 2011 24/09/2018
18 29832 Mr. Subham Bhakta Male University of Goettingen. PhD Chennai Mathematical Institute 2018  
19 29899 Mr. Rudra Narayan Padhan Male National institute of Technology, Rourkela PhD Indian Institute of Technology, Bombay 2015  
20 29953 Ms. Divya Aggarwal Female Indraprastha Institute of Information Technology PhD Student University of Delhi 2018  
21 29973 Mr. Saikat Maity Male University of Calcutta B.Sc complete year student      
22 29987 Ms. Sulakhana Chowdhury Female Indian Institute of Science Education and Research, Thiruvananthapuram IPhD Student ndian Institute of Science Education and Research, Thiruvananthapuram WebsiteDirections Save ndian Institute of Science Educatio   01/08/2019
23 30006 Ms Nishu Kumari Female Indian Institute of Science, Bangalore Ph.d IIT Kanpur 2018  
24 30017 Ms. Pauline Ezhilarasi A Female Stella Maris College Asst. Chennai Mathematical Institute 2013  
25 30050 Mr. Sujeet Bhalerao Male IISER Pune BS-MS student IISER Pune Appeared / Awaiting Result  
26 30082 Dr. Shameek Paul Male RKMVERI Assistant Professor University of Mumbai 2005 07/01/2012
27 30087 Mr Mohan R Male Indian Statistical Institute Bangalore Centre PhD Student Indian Institute of Technology Madras 2012  
28 30099 Dr. Suhas B N Male Amrita Vishwa Vidyapeetham, Bangalore Postdoctoral Fellow Bangalore 2010 14/03/2017
29 30116 Ms. Aroonima Sahoo Female National Institute Of Technology Rourkela PhD Student Utkal University, Odisha 2018  
30 30121 Dr. Debashish Bose Male Shiv Nadar University Asst. Prof. IIT Kanpur   31/12/2010
31 30123 Mr. Rahul Dattatraya Kitture Male IISER Mohali Post Doctoral Fellow Shivaji University Kolhapur 2008 16/12/2014
32 30125 Ms. Nupur Nandi Female National Institute Of Technology, Rourkela PhD Gangadhar Meher University, Sambalpur,768004, Odisha 2017  
Local       
1 29654 Mr. Sathish Kumar V Male The Institute of Mathematical Sciences PhD Ramanujan Institute for Advanced Study in Mathematics 2018  
2 29838 Mr. Ratheesh T V Male The Institute of Mathematical Sciences PhD Pazhasi Raja NSS College Mattanur 2017  
3 29881 Mr Sridhar Poojyam Narayanan Male Institute of Mathematical Sciences PhD BITS Pilani 2012  
4 30084 Mr. Siddheswar Kundu Male The institute of mathematical science JRF University of Calcutta 2018  
5 30092 Mr. Aritra Bhattacharya Male Institute of Mathematical Sciences PhD student Pune University 2018  

 

 

How to Reach: 

Click here

School Short Name: 

cmrt

Last Date Application: 

Friday, March 29, 2019

School Type: 

NCMW