Addendum to: A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices, by V. B. Mehta and Wilberd van der Kallen

TL;DR

This paper extends previous work on Frobenius splitting by demonstrating compatibility with additional subvarieties, inspired by an exercise in a well-known algebraic geometry book.

Contribution

It provides an addendum to earlier results, expanding the class of subvarieties compatible with Frobenius splitting techniques.

Findings

Extended Frobenius splitting compatibility to new subvarieties

Built upon earlier Frobenius splitting methods from 1992

Addressed an exercise from Brion Kumar's book

Abstract

Prompted by an exercise in the Brion Kumar book on Frobenius splittings, we show compatibility with a few more subvarieties of the Frobenius splitting from our 1992 paper.