Calabi-Yau techniques for Namikawa-Weyl groups

TL;DR

This paper develops a systematic method to determine Namikawa-Weyl groups for Calabi-Yau-2 algebra representation spaces, integrating categorical Calabi-Yau techniques and symmetry analysis, with applications to quiver varieties.

Contribution

It introduces a new strategy combining local-to-global functors and $A_{ abla}$-methods to compute Namikawa-Weyl groups in Calabi-Yau settings.

Findings

Successfully applied to quiver varieties

Recovered Yaochen Wu's results

Established a general computational framework

Abstract

The field of symplectic singularities aims to build a 21st century Lie theory. A key development is the Namikawa-Weyl group, which generalizes the classical Weyl group of Lie algebras. Another cornerstone is the integration of categorical Calabi-Yau techniques, capturing the rich algebraic structure of these singularities. In this paper, we develop a systematic strategy to determine Namikawa-Weyl groups for representation spaces of Calabi-Yau-2 algebras, leveraging local-to-global functors, symmetry analysis, and $ A_{\infty} $-methods. Applying this approach to quiver varieties, we carry out the detailed calculations and recover Yaochen Wu's result.