Characteristic cycles of highest weight Harish-Chandra modules

TL;DR

This paper determines the characteristic and leading term cycles of irreducible highest weight Harish-Chandra modules with regular integral infinitesimal character, highlighting differences between simply laced and nonsimply laced cases.

Contribution

It provides a detailed analysis of characteristic cycles for these modules, revealing their irreducibility in simply laced cases and complexity in nonsimply laced cases.

Findings

Characteristic cycles are irreducible in simply laced cases.

Characteristic cycles are more complicated in nonsimply laced cases.

The paper advances understanding of Harish-Chandra modules' geometric properties.

Abstract

Characteristic cycles and leading term cycles of irreducible highest weight Harish-Chandra modules of regular integral infinitesimal character are determined. In the simply laced cases they are irreducible, but in the nonsimply laced cases they are more complicated.