Vanishing cycles and Cartan eigenvectors

TL;DR

This paper explores the relationship between vanishing cycles of simple singularities and the eigenvectors of Cartan matrices, including their q-deformations, revealing new insights into their structure.

Contribution

It introduces a novel approach linking singularity theory with the eigenstructure of Cartan matrices and their q-deformations.

Findings

Identifies connections between vanishing cycles and Cartan eigenvectors.

Provides new methods for analyzing q-deformed Cartan matrices.

Enhances understanding of singularity-related algebraic structures.

Abstract

Using the vanishing cycles of simple singularities, we study the eigenvectors of Cartan matrices of finite root systems, and of q-deformations of these matrices.