Fall 2019

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

algebraic combinatorics,

representation theory,

Lie theory,

quantum groups,

and statistical mechanical models.