Last week I updated Hyperkaehler.info a bit, and now it also contains information on:

Especially the latter is really cool, it is a refinement of the Hodge decomposition using the representation theory of a finite-dimensional Lie algebra attached to a hyperkähler variety. Jieao Song created an interactive visualization of this decomposition, and this is now integrated into the website. You can explore it for type K3[4]. Notice how each type now also has its own canonical URL!

Full disclosure: I have used LLMs (more precisely, Claude Opus and Sonnet, via GitHub Copilot) to implement these additions. What would probably have taken me more than a day of work (including various unrelated fixes) ended up taking only one or two hours, split between some implementation work of my own and a larger amount of reviewing LLM-generated code.

It seems that LLMs have reached sufficient maturity to be useful for these things (but one has to carefully review things! they are basically very good autocomplete machines behaving like slot machines, or vice versa) and I'll be describing some more successful use cases later.