Complete branching rulesAlgebra & Discrete Mathematics
|Ricky Liu, NCSU
|Mon, Nov 3 2014, 1:10PM
Given an arbitrary diagram of boxes, one can define a representation of the symmetric group called a Specht module. For partitions, the corresponding Specht modules are irreducible, and their restrictions satisfy a simple branching rule. We will define an analogous notion of (complete) branching for arbitrary Specht modules and give a combinatorial criterion for when a diagram admits a complete branching rule. We will also relate this notion to questions in combinatorics, algebra, and geometry.