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).

Textbooks:

- Richard Stanley, Enumerative Combinatorics Volume 2
- I.G.Macdonald, Symmetric Functions and Hall Polynomials, second edition

credits:

3 (N-A)

semester:

InFrequent

prereqs:

741