A geometric study of BZ operator on representations of ${\mathrm{G}\mathrm{L}}_n$ over non-archimedean field

In this article, we geometrically study the partial Bernstein-Zelevinsky operator introduced in the author’s thesis, which generalizes the original Bernstein-Zelevinsky operator. We relate the partial Bernstein-Zelevinsky operator to the geometric induction of Lusztig and then perform explicit computations in special cases. Finally, we develop a symmetric reduction to the previously mentioned special cases