Advances in Lie Theory, Representation Theory, and Combinatorics: Inspired by the work of Georgia M. Benkart: "Great Permutations"
Presenter
May 3, 2024
Keywords:
- Lie algebras
- Representation theory
- combinatorics
MSC:
- 05-XX - Combinatorics
- 16-XX - Associative rings and algebras
- 17-XX - Nonassociative rings and algebras
- 20-XX - Group theory and generalizations
Abstract
Great Permutations is a coming-of-age tale that charts the progress of the permutation representation of the symmetric group as it navigates its way through a world of tensor products. This is simultaneously a story about the multiplicity of simple modules and the dimension of centralizer modules. Throughout, various shadowy intrigues such as walks on graphs, set-partition diagrams, and even classical invariant theory enliven the story. As a sequel to the plenary talk, A Tale of Two Groups, given by Georgia Benkart at the 1994 Joint Mathematics Meetings, Great Permutations is a feel-good tale of redemption through Schur-Weyl duality that is apt to bolster your faith in representation theory.