# Algebra Seminar

Speaker:
O'Neill Kingston, Iowa State University
Topic:
Crystal structure on Gelfand-Tsetlin-Zhelobenko patterns

Abstract:
In  this  talk,  we  begin  by  presenting  the  crystal  structure  of  finite-dimensional  irreducible  representations  of  the  Lie algebras $\mathfrak{sl}_n$ in terms of Gelfand-Tsetlin patterns.  We then define a crystal structure using the set of symplectic Zhelobenko patterns,  parametrizing bases for finite-dimensional irreducible representations of $\mathfrak{sp}_4$.  This is obtained by a bijection with Kashiwara-Nakashima tableaux and the symplectic jeu de taquin of Sheats and Lecouvey.  We offer some conjectures on the generalization of this structure to rank $n$.

Event Date:
October 7, 2019 - 3:30pm to 4:20pm
Location:
217 MLH
Calendar Category:
Seminar
Seminar Category:
Algebra