[Math] Reference request for studying Lie group & Lie algebra representations

Question

I am learning representation theory of Lie groups & Lie algebras from the book by Brian Hall. Unfortunately, this does not discuss infinite dimensional representations. Which books should I study for this when I complete my study of Brian Hall's book?

Answer 1

The following lecture notes of James E. Humphreys on "Representations of Semisimple Lie Algebras in the BGG Category O" might be interesting for you, also including infinite-dimensional representations of finite-dimensional Lie algebras, and much more: http://www.math.umass.edu/~jeh/bgg/main.pdf.