Wednesday, February 19, 10:007.527
Pavel Turek (Royal Holloway, University of London), Modular plethysms in the stable module category of SL₂(F_p) in characteristic p.

Abstract:
Schur functors ∇^{λ} are endofunctors in categories of modules of an algebra. Among others, they can be used to construct all polynomial representations of GL(V) in characteristic 0 and the Schur polynomials. A long-standing question asks to describe compositions of Schur functors, the so-called modular plethysms. We consider this question for the natural two-dimensional module of SL₂(F_p) in characteristic p when the modular plethysms behave particularly nicely and classify all 'small' modular plethysms which are projective and 'almost-projective'. Using endotrivial modules we then find the stable representation ring of SL₂(F_p) and describe how Schur functors act on all indecomposable modules of SL₂(F_p) .