Special Topics-Hecke Algbra, Fall 2015

MA 792-002 Introduction to Hecke Algebra

Fall 2015
Instructor: Naihuan Jing
TH 11:45--1:00 ; Classroom: SAS 1218

Course Description:
  Representation Theory uses matrix method to study algebraic structures such as groups, algebras, and in particular Lie algebras and Lie groups. It is widely used in many mathematical researches,
The importance can be partly explained by the fact that the subject has been associated with famous names such as Frobenius, Schur, Weyl, Langlands etc.
The subject is closely related to combinatorics, number theory, algebraic geometry, algebraic number theory, etc. We will review basic materials on the symmetric groups and then move to discuss representations of Hecke algebras, and affine Hecke algebras in connection with Lie algebras. Everyone interested in Combinatorics and Lie algebras will find this course useful in his/her research. 
Students with maturity in linear algebra and elementary group theory will have sufficient background for the course.  I will try to build the materials from scratch and present the course in a down-to-earth fashion.

There will be no formal textbooks and the materials are drawn from the following:
1) W. Fulton and J. Harris, Representation theory, A first course, GTM, Springer-Verlag, 1991.
2) Dipper and James, Proc. London Math Soc. 52 (1986), 20-52; M. Jimbo, LMP, 11 (1986), 247; LMP 10 (1985), 63.
3) Several online materials on symmetric groups and Hecke algebras. Also we will read some papers.
4) M. Geck and G. Pfeiffer, Characters of Finite Coxeter groups and Iwahori-Hecke algebras