Not offered in 2017-2018.
Steven Sam (Spring 2017):
Introduction to theory of symmetric functions and their applications to algebra. This course should be of interest to those who have an interest in combinatorics, representation theory, and/or algebraic geometry. Among the basic topics we will cover:
- Schur functions,
- Robinson-Schensted-Knuth correspondence,
- Littlewood-Richardson rule
For advanced topics, we will cover some subset of these possible topics:
- basic connections to representation theory (ordinary representations of symmetric groups, polynomial representations of complex general linear groups),
- Schubert calculus on Grassmannians,
- Hall-Littlewood polynomials and other connections to representation theory (ordinary representations of general linear groups over finite fields, projective representations of symmetric groups).
- Richard Stanley, Enumerative Combinatorics Volume 2
- I.G.Macdonald, Symmetric Functions and Hall Polynomials, second edition