Discretization of Springer fibers

TL;DR

This paper proposes new conjectural descriptions for the discretization of Springer fibers and their PBW analogues, aiming to facilitate computational approaches in Lie algebra representation theory.

Contribution

It introduces a novel conjectural framework for discretizations of Springer fibers and their PBW analogues, improving computational accessibility.

Findings

Proposed a conjectural description of Springer fiber discretization.

Introduced a conjectural PBW analogue of the discretization.

Differed substantially from previous discretization models.

Abstract

Consider a nilpotent element e in a simple complex Lie algebra. The Springer fibre corresponding to e admits a discretization (discrete analogue) introduced by the author in 1999. In this paper we propose a conjectural description of that discretization which is more amenable to computation. We also propose a conjectural PBW analogue of that discretization. This version differs substantially from the previous one.