On the Ext algebras of parabolic Verma modules and [formula omitted]-structures

Abstract

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 ( g l n + m , g l n ⊕ g l 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 ∞ -structure of a minimal model. An example of higher multiplications with non-vanishing m 3 is included.