# Nikolaus conference 2016

Speaker: Mikaël Cavallin (Kaiserslautern)

Title: On Orthogonal Embeddings and Irreducible Triples

Abstract:

In 1987, Seitz gave a complete classification of triples $$(Y,X,V),$$ where $$Y$$ is a simple group of classical type, $$X$$ is a maximal, closed, connected subgroup of $$Y,$$ and $$V$$ is a finite-dimensional, restricted, irreducible $$KY$$-module. Recently, we observed that in the case where $$Y=Spin_{2n+2}(K$$) and $$X=Spin_{2n}(K),$$ a family of examples was missing from the list. In this talk, I would like to show how certain methods, initially introduced by Ford, can be used to obtain all irreducibles $$V$$ as above for this embedding. This is joint work with Testerman.