Title: Crystal Bases in Algebraic Combinatorics
Course No. 846
Time: MWF 1:20
Instructor: Paul Terwilliger
Prerequisite: Good understanding of linear algebra.
Textbook: Crystal Bases, by Daniel Bump and Anne Schilling.
World Scientific, 2017.
ISBN: 978 981 473 3441
DESCRIPTION: A crystal base is a purely combinatorial
object that is used to describe representations of Lie
algebras and quantum groups. In this introductory course,
we will develop the theory of crystal bases from first principles,
and see how they get used in representation theory.
Along the way we will encounter topics such as:
root systems, Kashiwara crystals, Young tableaux and their crystals,
Stembridge crystals, insertion algorithms, bicrystals and the
Littlewood-Richardson rule, crystals for Stanley symmetric functions,
and Gelfand-Tsetlin patterns.
This course is suitable for first year graduate students.
It is recommended for anyone interested in
and statistical mechanical models.