Syllabus 280-2: Combinatorics and Representation Theory
Fall 2003

Lectures: M 2:10-3:00pm, R 8:30-10:20 in Kerr 593
Instructor: Anne Schilling, Kerr Hall 578, phone: 754-9371,
Text: Some of the material will be based on the following books:
  • B.E. Sagan, The symmetric group, second edition, Graduate Texts in Mathematics, Springer
  • L. Manivel, Symmetric functions, Schubert polynomials and degeneracy loci, SMFAMS vol. 6, American Math. Soc.
  • I.G. Macdonald, Notes on Schubert polynomials, Publications du Laboratoire de Combinatoire et d' Informatique Mathematique, Volume 6
We will also use recent papers which I will hand out or announce in class.
Grading: Every registered student is required to present a paper in class. A list of suitable papers and topics will be discussed in class.

Course description

This course will start from scratch (background on the symmetric group and symmetric functions will be helpful, but not required). Topics include:
symmetric group, Bruhat order, Schubert polynomials, Grassmannians, rc-graphs, Yang-Baxter equations, quiver varieties.