The course will be an introduction to Young tableaux and their application to the finite-dimensional representation theory of the group of n-by-n invertible matrics over the fields of real and complex numbers. We will study the geometry and representation theory of this group and discuss the links between them.

This course will serve both as a follow-up to the graduate level combinatorics course taught in 2005-2006 and as an introduction to the course in Schubert Varieties to be offered in Spring 2007.

Text: Young Tableaux: With Applications to Representation Theory and Geometry. London Math. Soc. Student Texts. New York: Cambridge University Press, 1997.

Prerequisites: Mathematical maturity at the level of a graduate student in mathematics.