Representation theory of quantized Gieseker varieties, I

TL;DR

This paper explores the representation theory of quantized Gieseker varieties, detailing categories of representations, homological properties, and localization theorems for various parameters.

Contribution

It provides a comprehensive analysis of the categories of finite dimensional representations and category O for quantized Gieseker varieties, including parameter conditions and ideal structures.

Findings

Categories of finite dimensional representations are classified for all parameters.

Parameters with finite homological dimension are identified.

Annihilators of irreducible objects in category O are determined for specific subgroups.

Abstract

We study the representation theory of quantizations of Gieseker moduli spaces. We describe the categories of finite dimensional representations for all parameters and categories O for special values of parameters. We find the values of parameters, where the quantizations have finite homological dimension, and establish abelian localization theorem. We describe the two-sided ideals. Finally, we determine annihilators of the irreducible objects in categories O for some special choices of one-parameter subgroups.