An Introduction to Plethysm
Channel: Amritanshu Prasad
Date: 2020-05-18

Plethysm of symmetric functions 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.


00:00:00 - The idea behind plethysm
00:30:40 - Axiomatic definition of plethysm
00:42:24 - Example: computation of f∘(-g)
00:53:00 - Example: computing ω(f∘g)
01:04:33 - Coproduct on symmetric functions
01:22:12 - f∘(g1+g2)