A new Weyl group action related to the quasi-classical Gelfand-Graev action

TL;DR

This paper constructs a Weyl group action on DKS type varieties, providing a quiver theoretic explanation for the quasi-classical Gelfand-Graev action, linking algebraic group symmetries with quiver varieties.

Contribution

It introduces a new Weyl group action on DKS type varieties, connecting it to the Gelfand-Graev action through quiver theory, which was not previously established.

Findings

Weyl group action constructed on DKS type varieties

Quiver theoretic explanation for Gelfand-Graev action

Enhanced understanding of symmetries in quiver varieties

Abstract

We construct a Weyl group action on the DKS type varieties, a certain class of varieties associated with quivers. As a result, on some special DKS type varieties, we can give a quiver theoretic explanation of the quasi-classical Gelfand-Graev action discovered by Ginzburg and Riche and studied by Ginzburg and Kazhdan recently.