## Department Seminar

## Understanding a Family of Representations of a Lie Algebra with Partitions, Graphs, and Recursion

## Dr. Lisa Schneider '10

### Salisbury University

### November 28, 2018

3:00-4:00

### Room: 309 Knott Hall

Abstract:
As a way to understand algebraic objects, representation theory is the study of algebraic objects using linear algebra techniques. Since representations of affine and quantum affine Lie algebras are difficult to study, a tractable avenue is the study of related representations of a current algebra. In this talk, we will discuss a specific family of representations of the current algebra for two-by-two trace zero matrices. One approach to studying representations is the use of combinatorial tools and objects. Through this lens, partitions with a prescribed set of rules and allowed moves provide a concrete understanding of one relationship between representations in this family. A deep understanding of this “game” corresponds to knowledge of how different representations in the specified family are related.

This talk will be accessible to Juniors and Seniors.

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