This is a continuation of a previous post.  Recall that we wanted to prove the following claim:

Claim.  Let \(\rho\) be a representation of \(SL_4\) such that no irreducible subrepresentation of \(\rho\) descends to \(SL_4/\mu_2\).  Then if \(\rho\) is self-dual, we have that $$8\mid\dim \rho.$$

I'm at UGA for the week, in between SWAG and TAAAG.  Today Danny Krashen gave a great talk on this paper of Auel, First, and Williams.  The paper is one of the latest in a long tradition of papers which construct counterexamples by making a topological computation and then approximating the relevant topological spaces by algebraic varieties.  (To my knowledge, this technique began with Totaro, but it has been exploited to great effect by Antieau, Williams, and most recently, fellow Ravi student Arnav Tripathy.) ...