Harish-Chandra bimodules over quantized flower quiver varieties with minimal support

TL;DR

This paper classifies minimal support Harish-Chandra bimodules over quantized flower quiver varieties, revealing a factorial count of such bimodules for certain parameters and none otherwise, using an advanced restriction functor.

Contribution

It provides a complete classification of minimal support Harish-Chandra bimodules in this setting, introducing an enhanced restriction functor as a key tool.

Findings

Number of minimal support bimodules equals n! for certain parameters

No such bimodules exist for other parameters

Classification depends on the dimension vector and quantization parameters

Abstract

We classify Harish-Chandra bimodules over the quantized flower quiver varieties with minimal support. We show that if the dimension vector is $n$, then there are $n!$ minimally supported simple Harish-Chandra bimodules for integral quantization parameters that are large enough or small enough, and there are none for other quantization parameters. The main tool used for this classification is an enhanced version of restriction functor.