Partial Implosions and Quivers

TL;DR

This paper introduces magnetic quivers for partial implosion spaces associated with parabolic subgroups, verifying conjectures in specific cases and extending understanding of nilpotent orbit closures in geometric representation theory.

Contribution

It proposes a new framework of magnetic quivers for partial implosions and verifies conjectures in subregular and hook diagram cases, advancing the study of implosion spaces.

Findings

Verification of the conjecture in subregular cases via Levi group reduction

Successful verification for hook diagram cases with nonzero Fayet-Iliopoulos parameters

Extension of partial implosion theory to broader classes of parabolic subgroups

Abstract

We propose magnetic quivers for partial implosion spaces. Such partial implosions involve a choice of parabolic subgroup, with the Borel subgroup corresponding to the standard implosion. In the subregular case we test the conjecture by verifying that reduction by the Levi group gives the appropriate nilpotent orbit closure. In the case of a parabolic corresponding to a hook diagram we are also able to carry out this verification provided we work at nonzero Fayet-Iliopoulos parameters.