A-infinity deformations of extended Khovanov arc algebras and Stroppel's conjecture

Abstract: Extended Khovanov arc algebras K_m^n are introduced by Stroppel when studying parabolic category O. They naturally appear in different subjects (including representation theory and symplectic geometry) and have many nice algebraic properties, for example they are Koszul and quasi-hereditary. In this talk, we will first give the diagrammatic description of K_m^n due to Brundan-Stroppel. Then, by writing K_m^n as the path algebra of a quiver with relations, we show that the Koszul dual of K_m^n admits a natural reduction system satisfying diamond condition, by relating the number of the associated "irreducible paths" to the Kazhdan-Lusztig polynomials. We also explain how to apply this reduction system to study Stroppel's conjecture. As a result, we show that K_m^n is not intrinsically formal for m, n>1. This is joint work with S. Barmeier.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: Meeting Link

uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09

Meeting ID: 918 7552 8987 Password: LAGOON2022

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

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