# Is there an accessible exposition of Gelfand-Tsetlin theory?

I'm hoping to start an undergraduate on a project that involves understanding a bit of Gelfand-Tsetlin theory, and have been tearing my hair out looking for a good reference for them to look at. Basically what I would want is something at the level of Vershik-Okounkov - A new approach to the representation theory of symmetric groups. 2 (or the book Ceccherini-Silberstein, Scarabotti, and Tolli - Representation theory of the symmetric groups based on it) but for finite dimensional representations of $$\mathrm{GL}_n$$. I feel like such a book or at least some expository notes should exist, but I have had zero luck finding any.

• Perhaps such a reference doesn't exist, especially if you and Tim have both looked for it and not found it. If it did exist, it would probably be within the scope of the Graduate Journal of Mathematics, gradmath.org, which "publishes original work as well as expository work [that] helps make more widely accessible significant mathematical ideas, constructions or theorems." One option would be to have your student write up the sort of thing you're looking for and submit it to GJM. The website says "High quality senior theses will find GJM to be a great venue" – David White Nov 14 at 18:00
• How about the Allen's notes from when he taught Lie groups in 2001-2002? I remember there was one on Gelfand-Tsetlin (or Gelfand-Cetlin as Allen spelled it). Those notes aren't online anymore, but hopefully Allen still has a copy. – Joel Kamnitzer Dec 8 at 4:40
• @JoelKamnitzer I found some notes on Allen’s website, but they were not really the style I was looking for. In particular, they assumed a lot of familiarity with the WCF in a way that didn’t really match what I had in mind. – Ben Webster Dec 11 at 1:42