On the Ext algebras of parabolic Verma modules and A infinity-structures

Details On the Ext algebras of parabolic Verma modules and A infinity-structures On the Ext algebras of parabolic Verma modules and A infinity-structures

2011-06-27

arxiv.org/abs/1106.5406v1

Mathematics

Representation Theory

This article is based on arXiv:1104.0102 and focuses on presenting the main results and techniques; Journal of Pure and Applie

Scientific paper

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.

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