Koszul Duality and Soergel Bimodules for Dihedral Groups

TL;DR

This paper demonstrates that the endomorphism ring of the projective generator in the category of Soergel modules for dihedral groups exhibits Koszul self-duality, revealing a deep algebraic symmetry.

Contribution

It establishes the Koszul self-duality of the endomorphism ring in the category of Soergel modules specifically for dihedral groups.

Findings

Endomorphism ring is Koszul self-dual.

Provides new insights into the structure of Soergel modules for dihedral groups.

Enhances understanding of algebraic symmetries in representation theory.

Abstract

We show that the endomorphism ring of the projective generator in the category of Soergel modules (for dihedral groups) is Koszul self-dual.