Started reading [Procesi] to learn invariant theory and representation theory because it came up quite often as my bottleneck in my recent work (eg). Also interpretability, apparently. So far I just read pg 1-9, reviewing the very basics of group action (e.g., orbit stabilizer theorem). Lie groups aren’t coming up until pg ~50 so until then I should catch up on the relevant Lie group prerequisites through [Lee] or [Bredon].
Woit’s “Quantum Theory, Groups and Representations” is fantastic for this IMO. It gives physical motivation for representation theory, connects it to invariants and, of course, works through the physically important lie-groups. The intuitions you build here should generalize. Plus, it’s well written.
Also, if you are ever in the market for differential topology, algebraic topology, and algebraic geometry, then I’d recommend Ronald Brown’s “Topology and Groupoids.” It presents the basic material of topology in a way that generalizes better to the fields above, along with some powerful geometric tools for calculations.
Thanks for the recommendation! Woit’s book does look fantastic (also as an introduction to quantum mechanics). I also known Sternberg’s Group Theory and Physics to be a good representation theory & physics book.
I did encounter Brown’s book during my search for algebraic topology books but I had to pass it over Bredon’s because it didn’t develop the homology / cohomology to the extent I was interested in. Though the groupoid perspective does seem very interesting and useful, so I might read it after completing my current set of textbooks.
No worries! For more recommendations like those two, I’d suggest having a look at “The Fast Track” on Sheafification. Of the books I’ve read from that list, all were fantastic. Note that site emphasises mathematics relevant for physics, and vice versa, so it might not be everyone’s cup of tea. But given your interests, I think you’ll find it useful.
Woit’s “Quantum Theory, Groups and Representations” is fantastic for this IMO. It gives physical motivation for representation theory, connects it to invariants and, of course, works through the physically important lie-groups. The intuitions you build here should generalize. Plus, it’s well written.
Also, if you are ever in the market for differential topology, algebraic topology, and algebraic geometry, then I’d recommend Ronald Brown’s “Topology and Groupoids.” It presents the basic material of topology in a way that generalizes better to the fields above, along with some powerful geometric tools for calculations.
Both author’s provide free pdfs of their books.
Thanks for the recommendation! Woit’s book does look fantastic (also as an introduction to quantum mechanics). I also known Sternberg’s Group Theory and Physics to be a good representation theory & physics book.
I did encounter Brown’s book during my search for algebraic topology books but I had to pass it over Bredon’s because it didn’t develop the homology / cohomology to the extent I was interested in. Though the groupoid perspective does seem very interesting and useful, so I might read it after completing my current set of textbooks.
No worries! For more recommendations like those two, I’d suggest having a look at “The Fast Track” on Sheafification. Of the books I’ve read from that list, all were fantastic. Note that site emphasises mathematics relevant for physics, and vice versa, so it might not be everyone’s cup of tea. But given your interests, I think you’ll find it useful.