Primitive ideals in quantum SL(3) and GL(3)

TL;DR

This paper explicitly determines generators for all primitive ideals in the quantized coordinate rings of 3x3 special and general linear groups, revealing their algebraic properties and structure.

Contribution

It provides the first complete explicit generating sets for primitive ideals in these quantum groups, extending previous partial results.

Findings

Generators form polynormal regular sequences

Primitive factor algebras are Auslander-Gorenstein and Cohen-Macaulay

All primitive ideals are explicitly described

Abstract

Explicit generating sets are found for all primitive ideals in the generic quantized coordinate rings of the 3x3 special and general linear groups over an arbitrary algebraically closed field. (Previously, generators were only known up to certain localizations.) The generating sets form polynormal regular sequences, from which it follows that all primitive factor algebras of these quantized coordinate rings are Auslander-Gorenstein and Cohen-Macaulay.