Speaker: Mikael Cavallin (Lausanne)

Title: Branching Problems for Representations of Simple Algebraic Groups

Abstract:

Let $$Y$$ be a simply connected simple algebraic group of classical type over an algebraically closed field $$K$$ of characteristic $$p\geq 0.$$ Also let $$X$$ be a closed connected subgroup of $$Y$$ and consider a non-trivial irreducible $$p$$-restricted rational $$KY$$-module $$V.$$ In this talk, we investigate the triples $$(Y,X,V)$$ such that $$X$$ acts with exactly two composition factors on $$V$$ and see how it generalizes a question initially investigated by Dynkin in the 1950s (for $$K=\mathbb{C}$$), and then Seitz in the 1980s (for $$K$$ arbitrary).