Conference abstracts

Session S08 - Lie Groups and Representations

July 28, 17:30 ~ 18:10

## Positivity of parabolic Kazhdan-Lusztig polynomials

### Universidad de Chile, Chile   -   nlibedinsky@gmail.com

We give diagrammatic categorifications of the spherical and of the anti-spherical modules for any Coxeter group. Our main theorem gives a “light leaves” basis of morphisms in these categorifications. We deduce that all flavours of parabolic Kazhdan-Lusztig polynomials have positive coefficients (for arbitrary choices of subsets of simple reflections).

Joint work with Geordie Williamson (Max Planck Institut).