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

Angela Klamt; Catharina Stroppel

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

Representation Theory 2011-06-28 v1 Symplectic Geometry

Authors: Angela Klamt , Catharina Stroppel

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.

Keywords

Ext algebra parabolic Verma module A infinity-structure Bernstein-Gelfand-Gelfand category O Kazhdan-Lusztig combinatorics

Cite

@article{arxiv.1106.5406,
  title  = {On the Ext algebras of parabolic Verma modules and A infinity-structures},
  author = {Angela Klamt and Catharina Stroppel},
  journal= {arXiv preprint arXiv:1106.5406},
  year   = {2011}
}

Comments

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

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

Abstract

Keywords

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