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

TY - JOUR

T1 - On the Ext algebras of parabolic Verma modules and A infinity-structures

AU - Klamt, Angela

AU - Stroppel, Catharina

PY - 2012/2

Y1 - 2012/2

N2 - 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 (gln+m,gln⊕glm) 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 m3 is included.

AB - 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 (gln+m,gln⊕glm) 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 m3 is included.

KW - Faculty of Science

M3 - Journal article

SN - 0022-4049

VL - 216

SP - 323

EP - 336

JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

IS - 2

ER -