|Date: Friday, November 09, 2012
Location: 3866 East Hall (4:10 PM to 5:00 PM)
Title: The Loop Murnaghan-Nakayama Rule
Abstract: Classically, Schur functions form a linear basis of the ring of symmetric functions are are ubiquitous in combinatorics, representation theory, and geometry. Recently, in the study of total positivity in matrix loop groups, Lam and Pylyavskyy developed a 'loop' generalization of these classical objects with a simple combinatorial interpretation. The loop Schur functions appeared more recently and independently in the study of the conjectural GW/DT correspondence for orbifolds where they are related to generating functions of ideal sheaves on orbifolds.
In this talk I will introduce loop Schur functions along with some basic properties. I will describe my motivations for studying them, and I will present a direct combinatorial proof of the loop Murnaghan-Nakayama rule which was pivotal in proving the GW/DT for a certain class of orbifold targets.
Speaker: Dustin Ross
Institution: Colorado State U.