Alladi Ramakrishnan Hall

Webinar: Introduction to Plethysm

Amritanshu Prasad

IMSc

Plethysm is an operation of symmetric functions that was introduced by D E Littlewood. It finds application in a wide range of problems in algebraic combinatorics. For example, it can be used to understand the restriction of a representation of the GL(n) to its subgroup of permutation matrices.

In this expository talk I will motivate, and then define plethysm. I will then illustrate how it is computed by proving some formulas, such as plethysm of a negative and plethysm under the omega involution. A familiarity with symmetric functions will be helpful in understanding this talk.