An important topic in representation theory is understanding the relationship between different bases for the same representation. In this talk, we discuss our work showing upper triangularity of the change-of-basis matrix between the sl_3 web basis and Specht basis for irreducible symmetric group representations of three-row rectangular shape. Specht bases are classical in combinatorial representation theory. Web bases arise in the context of studying Lie algebra representations diagrammatically. We will focus on our combinatorial analysis of the expansion of Specht vectors in the sl_3 web basis. This is joint work with Julianna Tymoczko at Smith College.
Relating the Specht and sl_3 web bases
Heather M. Russell, University of RichmondAuthors: Heather M. Russell & Julianna S. Tymoczko
2022 AWM Research Symposium
Geometric and Categorical Aspects of Representation Theory and Related Topics