NCMW  Combinatorial models in Representation Theory (2019)
Speakers and Syllabus
 Module A (B Ravinder, CMI) Young tableaux and the representation theory of the Lie algebra sl_{n} C: Review of some aspects of the general theory of representations of complex semisimple Lie algebras, the special case of sl_{n} C, highest weights and partitions, irreducible characters in terms of semistandard Young tableaux, GelfandTsetlin 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 RobinsonSchensted correspondence, SchurWeyl duality.
 Module C (KN Raghavan and S Viswanath, IMSc) The Littelmann path model: Paths, root operators, LakshmibaiSeshadri 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, WeylKac 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 sl_{n} , such as partitions, LS paths, abacus, semiinfinite 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
 B Ravinder (BR), CMI
 Amritanshu Prasad (AP), IMSc
 K N Raghavan (KNR), IMSc
 S Viswanath (SV), IMSc
 R Venkatesh (RV), IISc
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 
11.301.00 Lecture 2 
2.003.30 Lecture 3 
4.005.00 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 