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The category of perverse sheaves on the disk is isomorphic to the category of diagrams $$E\substack{\substack{c\\\to}\\\substack{v\\\leftarrow}}F$$ With $E,V$ finite dimensional vector spaces, and the maps satisfying $cv+1_E$$cv+1_F$ and $vc+1_F$$vc+1_E$ are isomorphisms.

We have on the disk maps $f_k:\Delta\to \Delta:z\mapsto z^k$. Given a diagram $D$, corresponding to the perverse sheaf $P_D$, what is the diagram for $Rf_{k*}P_D$,$Rf_{k!}P_D$, $f_k^!P_D$ and $f_k^*P_D$?

The category of perverse sheaves on the disk is isomorphic to the category of diagrams $$E\substack{\substack{c\\\to}\\\substack{v\\\leftarrow}}F$$ With $E,V$ finite dimensional vector spaces, and the maps satisfying $cv+1_E$ and $vc+1_F$ are isomorphisms.

We have on the disk maps $f_k:\Delta\to \Delta:z\mapsto z^k$. Given a diagram $D$, corresponding to the perverse sheaf $P_D$, what is the diagram for $Rf_{k*}P_D$,$Rf_{k!}P_D$, $f_k^!P_D$ and $f_k^*P_D$?

The category of perverse sheaves on the disk is isomorphic to the category of diagrams $$E\substack{\substack{c\\\to}\\\substack{v\\\leftarrow}}F$$ With $E,V$ finite dimensional vector spaces, and the maps satisfying $cv+1_F$ and $vc+1_E$ are isomorphisms.

We have on the disk maps $f_k:\Delta\to \Delta:z\mapsto z^k$. Given a diagram $D$, corresponding to the perverse sheaf $P_D$, what is the diagram for $Rf_{k*}P_D$,$Rf_{k!}P_D$, $f_k^!P_D$ and $f_k^*P_D$?

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Operations on perverse sheaves on disk

The category of perverse sheaves on the disk is isomorphic to the category of diagrams $$E\substack{\substack{c\\\to}\\\substack{v\\\leftarrow}}F$$ With $E,V$ finite dimensional vector spaces, and the maps satisfying $cv+1_E$ and $vc+1_F$ are isomorphisms.

We have on the disk maps $f_k:\Delta\to \Delta:z\mapsto z^k$. Given a diagram $D$, corresponding to the perverse sheaf $P_D$, what is the diagram for $Rf_{k*}P_D$,$Rf_{k!}P_D$, $f_k^!P_D$ and $f_k^*P_D$?