  We study the Ext-algebra of the direct sum of all parabolic Verma modules in
the principal block of the Bernstein-Gelfand-Gelfand category O for the
hermitian symmetric pair $(\mathfrak{gl}_{n+m}, \mathfrak{gl}_{n} \oplus
\mathfrak{gl}_m)$ and present the corresponding quiver with relations for the
cases n=1, 2. The Kazhdan-Lusztig combinatorics is used to deduce a general
vanishing result for the higher multiplications in the A infinity-structure of
a minimal model. An explicit example of the higher multiplications with
non-vanishing $m_3$ is included.
