Poset structure of torus-invariant prime spectra of CGL extensions

TL;DR

This paper extends Yakimov's theorem by demonstrating that a broader class of CGL extensions also have torus-invariant prime spectra isomorphic to Bruhat order intervals, using an iterative construction method.

Contribution

It introduces a new procedure for constructing poset isomorphisms between prime spectra of CGL extensions and Bruhat order intervals of Coxeter groups.

Findings

Examples of CGL extensions with spectra isomorphic to Bruhat intervals

A new iterative method for constructing poset isomorphisms

Generalization of Yakimov's theorem to broader classes

Abstract

A key theorem of Yakimov's proves that the torus-invariant prime spectra of De Concini-Kac-Procesi algebras are isomorphic as partially ordered sets to corresponding Bruhat order intervals of Weyl groups. We present examples of more general Cauchon-Goodearl-Letzter (CGL) extensions which exhibit this same phenomenon. To accomplish this, we develop a procedure for iteratively constructing poset isomorphisms between torus-invariant prime spectra of CGL extensions and Bruhat order intervals of Coxeter groups.