Ideals in Deligne's Rep(O_\delta) and representations of orthosymplectic supergroups

Deligne defined a category Re⎯⎯⎯⎯⎯p(Oδ) that permits the simultaneous study of the tensor powers of the natural representations of the orthogonal/symplectic groups and the orthosymplectic supergroups. In this talk I will first give a definition of Deligne's category in terms of Brauer diagrams. Next, I will describe a classification of the indecomposable objects in Re⎯⎯⎯⎯⎯p(Oδ) via Young diagrams and their corresponding weight diagrams. I will then explain a recent classification of thick ideals in Re⎯⎯⎯⎯⎯p(Oδ), and the consequences of this classification in terms of representations of the orthosymplectic supergroups.