On the Ext algebras of parabolic Verma modules and A infinity-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 $({\mathfrak{gl}}_{n+m},{\mathfrak{gl}}_n\oplus {\mathfrak{gl}}_m)$ 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.

This article is based on arXiv:1104.0102 and focuses on presenting the main results and techniques; Journal of Pure and Applied Algebra, 2011

References in corpus (1)

• A-infinity structures on the algebra of extensions of Verma modules in the parabolic category O

Cited by in corpus (1)

• The $\mathrm{Ext}$-algebra of standard modules over dual extension algebras