Degenerate twisted traces on quantized Kleinian singularities of type A

TL;DR

This paper investigates the structure and dimension of twisted trace spaces on quantized Kleinian singularities of type A, focusing on the degenerate cases and their relation to automorphisms and quantization parameters.

Contribution

It provides a detailed analysis of degenerate traces and determines the dimension of twisted trace spaces based on automorphisms and quantization parameters, represented by a polynomial.

Findings

Dimension of twisted trace space depends on automorphism and quantization parameters.

Explicit polynomial P encodes the relationship between parameters and trace space dimension.

Characterization of non-degenerate versus degenerate traces in the quantized setting.

Abstract

We study the space of non-degenerate traces on quantized Kleinian singularities of type A by studying their complement, the degenerate traces. In particular, we find the dimension of the space of twisted traces as a function of the corresponding automorphism and the quantization parameters, encoded in a polynomial $P$.