  In this work we introduce the definition of Schwarzenberger bundle on a
Grassmannian. Recalling the notion of Steiner bundle, we generalize the concept
of jumping pair for a Steiner bundle on a Grassmannian. After studying the
jumping locus variety and bounding its dimension, we give a complete
classification of Steiner bundle with jumping locus of maximal dimension, which
all are Schwarzenberger bundles.
