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arXiv · 1106.5406

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

Angela Klamt·Catharina Stroppel
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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.

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Angela Klamt, Catharina Stroppel. 2011-06-27. On the Ext algebras of parabolic Verma modules and A infinity-structures. https://arxiv.org/abs/1106.5406

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