Sheila Sundaram: Plethystic inversion and representations of the symmetric group
Channel: Amritanshu Prasad
Date: 2020-07-03

In this talk we will survey the many instances of plethystic inversion that occur in the representation theory of the symmetric group Sn. Perhaps the first such formula is due to Cadogan. The Lie representation of Sn, arising from the free Lie algebra, appears here. We will discuss the equivalence of Cadogan's formula to Thrall's decomposition of the regular representation, and to many other phenomena in a wide variety of contexts. New decompositions of the regular representation will be presented. Some of this material appears in the following papers: arXiv:1803.09368 arXiv:2003.10700. arXiv:2006.01896