Uniform Steiner bundles on ${\mathbb{P}}^n$ and reflection functors

Abstract

Let $n\in {\mathbb{N}}_{\ge 2}$. We prove that for every $k\ge 4$ there exist uniform but non-homogeneous Steiner bundles on ${\mathbb{P}}^n$ of $k$-type with disconnected splitting type, and we further investigate almost-uniform Steiner bundles. Our approach relies on interpreting Steiner bundles as relative projective Kronecker representations and applying adjoint pairs arising from restriction, inflation, and reflection functors.

preliminary version; comments are welcome