18.318   M.I.T.   Spring 2004

Topics in Combinatorics:   Lie Theory and Combinatorics

Class meets: Tuesday, Thursday   11-12:30   room 2-102 First class: Tuesday, February 3

Instructor: Alexander Postnikov   apost at math   room 2-389

Course webpage: http://www-math.mit.edu/~apost/courses/18.318/


The course is devoted to combinatorial aspects of Lie theory. Many combinatorial objects and constructions such as Young tableaux, Schur symmetric polynomials, the Bruhat order, the Littlewood-Richardson rule, and many others came originally from representation theory. We will discuss these classical topics as well as some recent advances. Representation theory provides a source of interesting combinatorial problems and constructions. On the other hand, a combinatorial approach proves helpful for many difficult problems in representation theory.

The course will include the following topics:

The course will be accessible to first year graduate students. All required notions and definitions will be given. There are no any special prerequisites though some background in combinatorics and/or representation theory would be helpful. The course can serve as an introduction to Lie theory for combinatorialists or as an introduction to combinatorics for Lie theorists.

Course Level: Graduate

Texts: Recommended (but not required) textbooks are:

* W. Fulton, J. Harris: Representation Theory: A First Course, Springer-Verlag, 1991.
*   J. E. Humphreys: Reflection Groups and Coxeter groups, Cambridge University Press, 1990.
* R. P. Stanley: Enumerative Combinatorics, Vol 2, Cambridge University Press, 1999.

Problem Sets:

Useful links: