Reducible characteristic cycles of Harish-Chandra modules for U(p,q) and the Kashiwara–Saito singularity

Abstract

We give examples of reducible characteristic cycles for irreducible Harish-Chandra modules for U (p, q) by analyzing a four-dimensional singular subvariety of C 8 . We relate this singularity to the Kashiwara-Saito singularity arising for Schubert varieties for GL(8, C) with reducible characteristic cycles, as well as recent related examples of Williamson. In particular, this gives another explanation of the simple highest weight modules for gl(12, C) with reducible associated varieties that Williamson discovered.