Rudolf Tange (University of Leeds) – Invariants in divided power algebras

This is based on the equally named paper which is on arxiv and to appear in Journal of Algebra. I will discuss the connection with the representations of reductive groups and Lie algebras: the hyper algebra, the restricted enveloping algebra and their centres. Then I will move to divided power algebras, truncated polynomial algebras and their invariants. I will discuss some results ($GL_n$ only) from my paper, a conjecture concerning the so-called “restriction property” and the connection with “special symmetrization map” from Okounkov-Olshanskii. If time allows, I will mention extensions of the above results to several matrices and vectors and covectors.