What happened to the fourth paper in the series "On the classification of primitive ideals for complex classical Lie algebras" by Garfinkle?

I am the author of this series of papers. Thank you for your interest in my work. I have continued to be active in math when I have had time for it, but most of my time in the past years has been taken with parenting responsibilities.

After completing the third paper, I began work on the fourth paper and made partial progress before setting it aside for an number of years, though I had hoped to return to it.

Because of interest in this work by researchers in this area, I had shared an incomplete draft of the fourth paper with some colleagues at their request. Last year, to my surprise, I discovered that a link to a modified version of that draft had been posted to this website. At my request, it has been taken down. To be totally clear, this version did not and does not have my authorization to have my name on it, nor to use my copyrighted content.

Meanwhile, I have been working on completing the fourth paper. While much of the proof parallels the argument in the third paper, there are new difficulties that need to be resolved. Many of them have to do with the fact that the Weyl group for type D_n is of index 2 in the Weyl group of type C_n. Thus, you have fewer pairs of tableaux to work with, and the proofs are a lot more difficult. However, as a result of recent progress, I am now optimistic that in the near future I will have a manuscript that can be posted to the arXiv.

It was written, but never published.

Tyson Gern's 2013 thesis references it:

• D. Garfinkle. On the classification of primitive ideals for complex classical Lie algebras, IV. unpublished.

Fortunately, the same thesis discusses the proof of the type $D$ case (page 41), and gives some extra references, including another article by Garfinkle, which are likely to be relevant.

You also might want to consider contacting the author of the thesis.

Gu's UROP+ paper "Nilpotent orbits: Geometry and combinatorics" references a recent version of the fourth paper of the series. Unfortunately, the referenced link is broken, so I'm not sure where the paper is accessible. You may want to contact William McGovern for a copy.