We describe \,
q-hypergeometric solutions of the equivariant quantum
differential equations and associated qKZ difference equations for the
cotangent bundle
T∗Fλ of a partial flag variety \,
Fλ\,.
These \,
q-hypergeometric solutions manifest a Landau-Ginzburg mirror symmetry
for the cotangent bundle. We formulate and prove Pieri rules for quantum
equivariant cohomology of the cotangent bundle. Our Gamma theorem for
\,
T∗Fλ \,says that the leading term of the asymptotics of the
\,
q-hypergeometric solutions can be written as the equivariant Gamma class of
the tangent bundle of
T∗Fλ multiplied by the exponentials of the
equivariant first Chern classes of the associated vector bundles. That
statement is analogous to the statement of the gamma conjecture by B.\,Dubrovin
and by S.\,Galkin, V.\,Golyshev, and H.\,Iritani, see also the Gamma theorem
for \,
Fλ \,in Appendix B.